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Lesson 10-1 Angle Relationships

Lesson 10-2 Complementary and Supplementary Angles

Lesson 10-3 Statistics: Display Data in a Circle Graph

Lesson 10-4 Triangles

Lesson 10-5 Problem-Solving Investigation: Use Logical Reasoning

Lesson 10-6 Quadrilaterals

Lesson 10-7 Similar Figures

Lesson 10-8 Polygons and Tessellations

Lesson 10-9 Translations

Lesson 10-10 Reflections

Five-Minute Check (over Chapter 9)Main Idea and VocabularyCalifornia StandardsExample 1: Naming AnglesKey Concept: Types of AnglesExample 2: Classify AnglesExample 3: Classify AnglesKey Concept: Vertical Angles and Adjacent AnglesExample 4: Real-World Example

• angle• degrees• vertex• congruent angles• right angle• acute angle

• Classify angles and identify vertical and adjacent angles.

• obtuse angle• straight angle• vertical angles• adjacent angles

Standard 6MG2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.

Naming Angles

Name the angle to the right.

Use the vertex as the middle letter and a point from each side. FGH or HGF

Use the vertex only.G

Use a number.2

The angle can be named in four ways: FGH, HGF, G, 2.

Naming Angles

Answer: FGH, HGF, G, 2

A. AB. BC. CD. D

0% 0%0%0%

A. RST

Which of the following is not a name for the angle below?

Classify Angles

Classify the angle as acute, obtuse, right, or straight.

Answer: The angle is exactly 180°, so it is a straight angle.

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. acute

B. obtuse

C. right

D. straight

Classify Angles

Answer: The angle is less than 90°, so it is an acute angle.

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. acute

B. obtuse

C. right

D. straight

Answer: 3 and 5 are vertical angles. 3 and 4 are adjacent angles. 4 and 5 are adjacent angles.

1. A2. B3. C4. D

0%0%0%0%

A B C D

For the figure shown, which of the following is true?

A.B.C.D.

Five-Minute Check (over Chapter 10-1)Main Idea and VocabularyCalifornia StandardsKey Concept: Complementary and Supplementary AnglesExample 1: Identify AnglesExample 2: Identify AnglesExample 3: Find a Missing Angle Measure

• complementary angle• supplementary angle

• Identify complementary and supplementary angles and find missing angle measures.

Homework:P. 516 – 517: 4-11 and 22 – 30CST: 1 - 5

Definition: An angle has two sides that share a common end point.

Definition: The point where the two sides meet is called the vertex.

Vertex

Definition: Angles are measured in degrees. 1 degree is one of 360 equal parts of a circle.

Protractor

1. FGH 2. HGF3. G4. 2

Definition: Angles are named in 4 different ways.

Right Angle

Acute Angle

Obtuse Angle

Straight Angle

Identify Angles

Classify the pair of angles as complementary, supplementary, or neither.

128° + 52° = 180°

Answer: The angles are supplementary.

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. complementaryB. supplementaryC. neitherD. acute

Identify Angles

x and y form a right angle.

Answer: So, the angles are complementary.

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. complementary

B. supplementary

C. neither

D. not enough information

Find a Missing Angle Measure

ALGEBRA Angles PQS and RQS are supplementary. If mPQS = 56°, find mRQS.

Words The sum of the measures of PQS and RQS is 180°.

Variable Let x represent the measure of RQS.

Equation 56 + x = 180

1. A2. B3. C4. D

0%0%0%0%

A B C D

C. 157

D. 337

Angles MNP and KNP are complementary. If mMNP = 23°, find mKNP.

Five-Minute Check (over Lesson 10-2)Main Idea and VocabularyCalifornia StandardsExample 1: Display Data in a Circle GraphExample 2: Construct a Circle GraphExample 3: Analyze a Circle GraphExample 4: Analyze a Circle Graph

• circle graph

• Construct and interpret circle graphs.

Reinforcement of Standard 5SDAP1.2 Organize and display single-variable data in appropriate graphs and representations (e.g., histogram, circle graphs) and explain which types of graphs are appropriate for various data sets.

Display Data in a Circle Graph

SPORTS In a survey, a group of middle-school students was asked to name their favorite sport. The results are shown in the table. Make a circle graph of the data.

Find the degrees for each part. Round to the nearest whole degree.

Use a compass to draw a circle with a radius marked as shown.

Then use a protractor to draw the first angle, in this case 108°.

Repeat this step for each section.

Check To draw an accurate circle graph, make sure the sum of the angle measures equals 360°.

Label each section of the graph with the category and percent. Give the graph a title.

Answer: Student’s Favorite Sports

ICE CREAM In a survey, a group of students was asked to name their favorite flavor of ice cream. The results are shown in the table. Make a circle graph of the data.

A. AB. BC. CD. D

0% 0%0%0%

Construct a Circle Graph

MOVIES Gina has the following types of movies in her DVD collection. Make a circle graph of the data.

Find the total number of DVDs: 24 + 15 + 7 or 46.

Find the ratio that compares each number with the total. Write the ratio as a decimal number rounded to the nearest hundredth.

Find the number of degrees for each section of the graph.

action: 0.52 ● 360 ≈ 187°comedy: 0.33 ● 360 ≈ 119°science fiction: 0.15 ● 360 ≈ 54°Draw the circle graph.

Check: After drawing the first two sections, you can measure the last section of the circle graph to verify that the angles have the correct measures.

Answer:

MARBLES Michael has the following colors of marbles in his marble collection. Make a circle graph of the data.

1. A2. B3. C4. D

0%0%0%0%

A B C D

Analyze a Circle Graph

VOTING The circle graph below shows the percent of voters in a town who are registered with a political party. Which party has the most registered voters?The largest section of the circle is the one representing Democrats. So, the Democratic party has the most registered voters.

Answer: Democrats

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. yesB. noC. no opinionD. not enough

information

SPORTS The circle graph below shows the responses of middle school students to the question, “Should teens be allowed to play professional sports?”. Which response was the greatest?

VOTING The circle graph below shows the percent of voters in a town who are registered with a political party. If the town has 3,400 registered Republicans, about how many voters are registered in all?

3,400 Republicans represents 42% of the registered voters.

3,400 = 42% of registered voters

There are 8,095 registered voters in all.

Answer: 8,095

3,400 = 0.42x Let x represented the number of

registered voters.

8,095 = x Simplify.

Divide each side by 0.42.

A. AB. BC. CD. D

0% 0%0%0%

A. 325

B. 415

C. 500

D. 625

If 275 students responded yes in the sports survey in example 3 your turn, how many students were surveyed in all?

Five-Minute Check (over Lesson 10-3)Main Idea and VocabularyCalifornia StandardsKey Concept: Angles of a TriangleExample 1: Find a Missing MeasureExample 2: Standards ExampleKey Concept: Classify Triangles Using Angles and SidesExample 3: Real-World ExampleExample 4: Draw TrianglesExample 5: Draw Triangles

• triangle• congruent segments• acute triangle• right triangle

• Identify and classify triangles.

• obtuse angle• scalene triangle• isosceles triangle• equilateral triangle

Standard 6MG2.2 Use the properties of complementary and supplementary angles and the sum of the angles of a triangle to solve problems involving an unknown angle.Standard 6MG2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle.)

Find a Missing Measure

ALGEBRA Find mA in ΔABC if mA = mB and mC = 80.

2x = 100 Simplify.

x = 50 Divide each side by 2.

Answer: The measure of mA is 50°.

2x + 80 = 180 x + x = 2x

x + x + 80 = 180 Write the equation.

–80 –80 Subtract 80 from each side.

A. AB. BC. CD. D

ALGEBRA Find mM in ΔMNO if mN = 75° and mO = 67.

75 + 67 + x = 180 142 + x = 180 –142 –142 x = 38CHECK:75 + 67 + 38 = 180

An airplane has wings that are shaped like triangles. What is the missing measure of the angle?A 41B 31C 26D 21

47 + 112 + x = 180

159 + x = 180 –159 –159 x = 21

CHECK:47 + 112 + 21 = 180

1. A2. B3. C4. D

A. 73°

B. 49°

C. 58°

D. 53°

SEWING A piece of fabric is shaped like a triangle. Find the missing measure.

73 + 58 + n = 180 131 + n = 180 –131 –131 n = 49

CHECK:73 + 58 + 49 = 180

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. acute

B. equilateral

C. right, scalene

D. obtuse, isosceles

Classify the triangle by its angles and its sides.

DRAWING TRIANGLES Susan has drawn a triangle with three acute angles and three congruent sides. Classify the triangle.

The triangle has three congruent sides. All three angles are acute.

Answer: So, it is an acute equilateral triangle.

Draw Triangles

A. AB. BC. CD. D

0% 0%0%0%

A. right equilateral

B. acute scalene

C. right scalene

D. acute equilaterla

DRAWING TRIANGLES Draw a triangle with one right angle and no congruent sides. Classify the triangle.

DRAWING TRIANGLES Phil has drawn a triangle with two acute angles and two congruent sides. Classify the triangle.

Answer: So, it is an obtuse isosceles triangle.

Draw Triangles

Because the triangle has two congruent sides, the triangle is isosceles. The triangle has two acute angles and one obtuse angle. Therefore, the triangle is obtuse.

A. AB. BC. CD. D

0% 0%0%0%

A. right isosceles

B. acute equilateral

C. right scalene

D. acute isosceles

DRAWING TRIANGLES Draw a triangle with three acute angles and two congruent sides. Classify the triangle.

Five-Minute Check (over Lesson 10-4)Main IdeaCalifornia StandardsExample 1: Use Logical Reasoning

• Solve problems by using logical reasoning.

Standard 6MR1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed. Standard 6MG2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle).

Use Logical Reasoning

NUMBER BALL Draw an isosceles triangle. How can you confirm that it is isosceles? Use logical reasoning.

Explore Isosceles triangles have two congruent sides. You need to find whether two of the sides are congruent.

Plan Select adequate method and measuring tools that will allow you to accurately measure the sides of the triangle.

Solve Measure and record the lengths of all three sides of the triangle.

Use Logical Reasoning

Check If two (or three) of the sides of the triangle have the same length then the triangle is an isosceles triangle. If none of the sides of the triangle are equal then the triangle is not an isosceles triangle.

Sample answer: I measured the sides and found that two (or three) of them have the same length.

A. AB. BC. CD. D

0% 0%0%0%

A. measure the acute angles

B. measure the hypotenuse

C. measure the right angleD. measure the legs

Draw a right triangle. How can you confirm that it is a right triangle?

Five-Minute Check (over Lesson 10-5)Main Idea and VocabularyCalifornia StandardsExample 1: Classify QuadrilateralsExample 2: Classify QuadrilateralsKey Concept: Angles of a QuadrilateralExample 3: Find a Missing Measure

• quadrilateral• parallelogram• trapezoid• rhombus

• Identify and classify quadrilaterals.

Standard 6MG2.3 Draw quadrilaterals and triangles from given information about them (e.g., a quadrilateral having equal sides but no right angles, a right isosceles triangle.)

Classify Quadrilaterals

Classify the quadrilateral using the name that best describes it.

Answer: The quadrilateral has 4 right angles and opposite sides are congruent. It is a rectangle.

A. AB. BC. CD. D

0% 0%0%0%

A. rectangle

B. parallelogram

C. trapezoid

D. square

Classify Quadrilaterals

Answer: The quadrilateral has one pair of parallel sides. It is a trapezoid.

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. rectangle

B. trapezoid

C. parallelogram

D. square

ALGEBRA Find the value of x in the quadrilateral shown.

Words The sum of the measures is 360°.

Variable Let x represent the missing measure.

Equation 60 + 120 + 60 + x = 360

60 + 120 + 60 + x = 360 Write the equation.

240 + x = 360 Simplify.

Answer: The missing angle measure is 120°.

x = 120

–240 –240 Subtract 240 from each side.

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. 68°

B. 109°

C. 134°

D. 226°

Find the missing angle measure in the quadrilateral.

Five-Minute Check (over Lesson 10-6)Main Idea and VocabularyCalifornia StandardsKey Concept: Similar FiguresExample 1: Identify Similar FiguresExample 2: Find Side Measures of Similar TrianglesExample 3: Real-World Example

• similar figures• corresponding sides• corresponding angles• indirect measurement

• Determine whether figures are similar and find a missing length in a pair of similar figures.

Identify Similar Figures

Which rectangle is similar to rectangle FGHI?

Find Side Measures of Similar Triangles

If ΔABC ~ ΔDEF, find the length of .

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. 9 in.B. 11.5 in.C. 13.5 in.D. 15 in.

If ΔJKL ~ ΔMNO, find the length of .

108 = 8n8 8

13.5 n=

108 = 8n

6 18· = 8· n

ARCHITECTURE A rectangular picture window 12-feet long and 6-feet wide needs to be shortened to 9 feet in length to fit a redesigned wall. If the architect wants the new window to be similar to the old window, how wide will the new window be?

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. 4 ftB. 6 ftC. 9 ftD. 10 ft

Tom has a rectangular garden which has a length of 12 feet and a width of 8 feet. He wishes to start a second garden which is similar to the first and will have a width of 6 feet. Find the length of the new garden.

Five-Minute Check (over Lesson 10-7)Main Idea and VocabularyCalifornia StandardsExample 1: Classify PolygonsExample 2: Classify PolygonsExample 3: Angle Measures of a PolygonExample 4: Real-World Example

• polygon• pentagon• hexagon• heptagon• octagon

• Classify polygons and determine which polygons can form a tessellation.

• nonagon• decagon• regular polygon• tessellation

Standard 6MR2.2 Apply strategies and results from simpler problems to more complex problems.Standard 6AF3.2 Express in symbolic form simple relationships arising from geometry.

Classify Polygons

Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular.

If it is not a polygon, explain why.

Answer: The figure is not a polygon since it has a curved side.

A. AB. BC. CD. D

0% 0%0%0%

A. polygon, regular

B. pentagon, not regular

C. not a polygonD. can’t tell

Classify Polygons

If it is not a polygon, explain why.

Answer: This figure has 6 sides which are not all of equal length. It is a hexagon that is not regular.

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. polygon, regularB. polygon, not regularC. not a polygonD. can’t tell

Angle Measures of a Polygon

ALGEBRA Find the measure of each angle of a regular heptagon. Round to the nearest tenth of a degree.

Draw all of the diagonals from one vertex and count the

number of triangles formed.

Angle Measures of a Polygon

Find the sum of the measures of the polygon.

Find the measure of each angle of the polygon. Let n represent the measure of one angle in the heptagon.

Answer: The measure of each angle in a regular heptagon is 128.6°.

number of triangles formed × 180°

sum of angle measures in polygon

5 × 180° 900°=

7n = 900 There are seven congruent angles.

n = 128.6 Divide each side by 7.

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. 90°

B. 104.2°

C. 120°

D. 132.8°

Find the measure of each angle in a regular hexagon.

PATTERNS Ms. Pena is creating a pattern on a wall. She wants to use regular hexagons. Can Ms. Pena make a tessellation with regular hexagons?The measure of each angle in a regular hexagon is 120°.The sum of the measures of the angles where the vertices meet must be 360°.

Since 120° divides evenly into 360°, the regular hexagon can be used.

Answer: yes

Interactive Lab:Tessellations

A. AB. BC. CD. D

0% 0%0%0%

A. yesB. noC. maybeD. not enough

information

QUILTING Emily is making a quilt using fabric pieces

shaped as equilateral triangles. Can Emily tessellate the quilt with these fabric pieces?

Five-Minute Check (over Lesson 10-8)Main Idea and VocabularyCalifornia StandardsExample 1: Graph a TranslationExample 2: Find Coordinates of a Translation

• transformation• translation• congruent figures

• Graph translations of polygons on a coordinate plane.

Preparation for Standard 7MG3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.

Graph a Translation

Translate ΔABC 5 units left and 1 unit up.

Move each vertex of the figure 5 units left and 1 unit up. Label the new vertices A, B,and C.

Answer: The coordinates of the vertices of the new figure are A'(–4, –1), B'(–1, 2), and C'(0, –1).

Connect the vertices to draw the triangle.

Interactive Lab:Translations

A. AB. BC. CD. D

0% 0%0%0%

Translate ΔDEF 3 units left and 2 units down.A. B.

Find Coordinates of a Translation

Trapezoid GHIJ has vertices G(–4, 1), H(–4, 3), I(–2, 3), and J(–1, 1). Find the vertices of trapezoid GHIJ after a translation of 5 units right and 3 units down. Then graph the figure and its translated image.

Find Coordinates of a Translation

Answer: The coordinates of trapezoid G'H'I'J' are G'(1, –2), H'(1, 0), I'(3, 0), and J'(4, –2).

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. M(–1, 0), N(1, –3), O(–4, –6)B. M(1, 0), N(–1, 3), O(4, 6)C. M(0, 1), N(3, –1), O(6, 4)D. M(1, 2), N(–3, –2), O(–4, 3)

Triangle MNO has vertices M(–5, –3), N(–7, 0), and O(–2, 3). Find the vertices of triangle MNO after a translation of 6 units right and 3 units up.

Five-Minute Check (over Lesson 10-9)Main Idea and VocabularyCalifornia StandardsExample 1: Real-World ExampleExample 2: Real-World ExampleExample 3: Real-World ExampleExample 4: Reflect a Figure Over the x-axisExample 5: Reflect a Figure Over the y-axis

• line symmetry• line of symmetry• reflection• line of reflection

• Identify figures with line symmetry and graph reflections on a coordinate plane.

Preparation for Standard 7MG3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to them, and determine their image under translations and reflections.

Determine whether the figure has line symmetry. If so, copy the figure and draw all lines of symmetry.

Answer: This figure has line symmetry. There are two lines of symmetry.

A. AB. BC. CD. D

0% 0%0%0%

A. one line of symmetryB. two lines of symmetryC. three lines of symmetryD. no line of symmetry

Determine whether the figure has line symmetry.

Answer: This figure has line symmetry. There is one line of symmetry.

1. A2. B3. C4. D

0%0%0%0%

A B C D

Answer: This figure does not have line symmetry.

1. A2. B3. C4. D

0%0%0%0%

A B C D

Quadrilateral QRST has vertices Q(–1, 1), R(0, 3), S(3, 2), and T(4, 0). Graph the figure and its reflected image over the x-axis. Then find the coordinates of the reflected image.

Reflect a Figure Over the x-axis

Plot the vertices and connect to form the quadrilateral QRST.

The x-axis is the line of symmetry. So, the distance from each point on quadrilateral QRST to the line of symmetry is the same as the distance from the line of symmetry to quadrilateral QRST.

Answer: Q(–1, –1) R(0, –3)S(3, –2) T(4, 0)

Reflect a Figure Over the x-axis

A. AB. BC. CD. D0% 0%0%0%

A. A(–2, –3), B(–5, –1), C(–3, 3), D(–1, 2)

B. A(0, 2), B(–1, 3), C(–2, 1), D(–4, 5)

C. A(–3, –2), B(–1, –5), C(3, –3), D(2, –1)

D. A(1, –3), B(–2, 4), C(3, –2), D(0, 0)

Quadrilateral ABCD has vertices A(–3, 2), B(–1, 5), C(3, 3), and D(2, 1). Find the coordinates of the reflected image over the x-axis.

Triangle XYZ has vertices X(1, 2), Y(2, 1), and Z(1, –2). Graph the figure and its reflected image over the y-axis. Then find the coordinates of the reflected image.

Reflect a Figure Over the y-axis

Plot the vertices and connect to form the triangle XYZ.

The y-axis is the line of symmetry. So, the distance from each point on triangle XYZ to the line of symmetry is the same as the distance from the line of symmetry to triangle XYZ.

Answer: X(–1, 2), Y(–2, 1), Z(–1, –2)

Reflect a Figure Over the y-axis

A. AB. BC. CD. D

0% 0%0%0%

A. Q(–2, 3), R(0, 1), S(–5, 1)

B. Q(3, –4), R(1, 0), S(6, –2)

C. Q(4, 3), R(0, 1), S(2, 6)

D. Q(–3, 4), R(–1, 0), S(–6, 2)

Triangle QRS has vertices Q(3, 4), R(1, 0), and S(6, 2).

Find the coordinates of the reflected image over the y-axis.

Five-Minute Checks

Image Bank

Math Tools

Tessellations

Translations

Lesson 10-1 (over Chapter 9) Lesson 10-2 (over Lesson 10-1)

Lesson 10-3 (over Lesson 10-2)

To use the images that are on the following three slides in your own presentation:1. Exit this presentation. 2. Open a chapter presentation using a

full installation of Microsoft® PowerPoint® in editing mode and scroll to the Image Bank slides.

3. Select an image, copy it, and paste it into your presentation.

A. AB. BC. CD. D

0% 0%0%0%

There are 12 balls in a hat and 3 are red. What is the probability of drawing a red ball?

(over Chapter 9)

1. A2. B3. C4. D

0%0%0%0%

A B C D

D. 120

Use the Fundamental Counting Principle to find the total number of outcomes when choosing an outfit from 3 pairs of pants, 5 shirts, and 4 jackets.

(over Chapter 9)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. 5,040

C. 10,080

D. 4,900

How many ways can 7 books be stacked in a single pile?

(over Chapter 9)

A. AB. BC. CD. D

0% 0%0%0%

A coin is tossed 14 times. It lands on heads 8 times and on tails 6 times. What is the theoretical probability of landing on tails? What is the experimental probability of the coin landing on tails?

(over Chapter 9)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A number cube is rolled and the spinner shown in the image is spun. What is the probability of rolling an even number and spinning an odd number?

(over Chapter 8)

A. AB. BC. CD. D

0% 0%0%0%

(over Lesson 10-1)

A. acute

B. obtuse

C. right

D. straight

1. A2. B3. C4. D

0%0%0%0%

A B C D

(over Lesson 10-1)

A. acute

B. obtuse

C. right

D. straight

1. A2. B3. C4. D

0%0%0%0%

A B C D

(over Lesson 10-1)

A. acute

B. obtuse

C. right

D. straight

A. AB. BC. CD. D

0% 0%0%0%

(over Lesson 10-1)

C. 102

D. 112

Find the value of x in the figure.

1. A2. B

A. true

B. false

Tell whether the following statement is true orfalse. A straight angle has a measure of 180°.

(over Lesson 10-1)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. 1 and 3

B. 2 and 3

C. 2 and 4

D. 3 and 1

Which of the angles shown in the diagram are adjacent?

(over Lesson 10-1)

Identify the pair of angles as complementary, supplementary, or neither.

(over Lesson 10-2)

0% 0%0%

1. A2. B3. C

A. complementary

B. supplementary

C. neither

(over Lesson 10-2)

0% 0%0%

1. A2. B3. C

A. complementary

B. supplementary

C. neither

(over Lesson 10-2)

0% 0%0%

1. A2. B3. C

A. complementary

B. supplementary

C. neither

A. AB. BC. CD. D

0% 0%0%0%

D. 145

Find the value of x.

(over Lesson 10-2)

1. A2. B

A. true

B. false

State whether the following statement is true or false. Angles are complementary if the sum of their measures is 180°.

(over Lesson 10-2)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. 33°

B. 43°

C. 57°

D. 123°

If 1 and 2 are complementary angles, and m1 is 57°, what is the measure of 2?

(over Lesson 10-2)

A. AB. BC. CD. D

0% 0%0%0%

Which choice shows a circle graph for the set of data in the table?

(over Lesson 10-3)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. 12.5%

B. 18.75%

C. 31.25%

D. 37.5%

Using the table, what percent of 7th graders who play sports are on the track and field team?

(over Lesson 10-3)

1. A2. B3. C

0% 0%0%

Find the missing measure in the triangle. Then classify the triangle as acute, right, or obtuse.

A. 127°; acute

B. 100°; obtuse

C. 90°; right

(over Lesson 10-4)

1. A.2. B.3. C.

0% 0%0%

Find the missing measure in the triangle. Then classify the triangle as acute, right, or obtuse.

A. 15°; acute

B. 15°; obtuse

C. 25°; right

(over Lesson 10-4)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. acute

B. equilateral

C. obtuse

D. scalene

Three sides of a triangle measure 3 centimeters, 4 centimeters, and 5 centimeters. Classify the triangle by its sides.

(over Lesson 10-4)

A. AB. BC. CD. D

0% 0%0%0%

A. acute

B. equilateral

C. obtuse

D. scalene

Two angles of a triangle measure 25° and 45°. Classify the triangle by its angles.

(over Lesson 10-4)

1. A2. B3. C4. D

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A B C D

A. No; it is not possible to classify the triangle by its side as the measurements of the sides are not given.

B. No; if all three angles of a triangle are 60°, then all three sides are not congruent, and the triangle cannot be classified.

C. Yes; if all three angles of a triangle are congruent, then all three sides are congruent, and the triangle is a right triangle.

D. Yes; if all three angles of a triangle are congruent, then all three sides are congruent, and the triangle is equilateral.

All three angles of a triangle measure 60°. Can you classify the triangle by its sides? Explain.

(over Lesson 10-4)

1. A2. B3. C4. D

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A B C D

A. equilateral

B. scalene

C. acute

D. right

Which of the following triangles could not be classified as isosceles?

(over Lesson 10-4)

A. AB. BC. CD. D0% 0%0%0%

A. red

B. blue

C. gray

D. white

Susan pulls out five socks in a drawer. There is a red sock, blue sock, black sock, white sock, and a gray sock. The first sock she pulls out is not blue. The last sock she pulls out is black. She pulls out the blue sock before she pulls out the red rock. The third sock she pulls out is not white or gray. The first sock she pulls out is either gray or red. What color is the third sock?

(over Lesson 10-5)

1. A2. B3. C4. D

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A B C D

B. Leah

C. Susan

D. Brian

Jo, Leah, Susan, and Brian are in line. Susan is before Brian, Jo is second, and Brian is not last. Who is last in line?

(over Lesson 10-5)

1. A2. B3. C4. D

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A B C D

A. 432 miles

B. 500 miles

C. 563 miles

D. 864 miles

On a family vacation, the Jacksons drove 995 miles in two days. On the first day they drove 131 more miles than the second day. How many miles did they drive on the first day?

(over Lesson 10-5)

A. AB. BC. CD. D

0% 0%0%0%

A. Complementary angles are acute.

B. Complementary angles’ sum is 90°.

C. Complementary angles’ sum is 180°.

D. Complementary angles are not right angles.

Which of the following statement is not true about complementary angles?

(over Lesson 10-5)

A. AB. BC. CD. D

0% 0%0%0%

A. square

B. rectangle

C. rhombus

D. trapezoid

(over Lesson 10-6)

1. A2. B3. C4. D

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A B C D

A. square

B. rectangle

C. rhombus

D. trapezoid

(over Lesson 10-6)

1. A2. B3. C

A. Sometimes; parallelograms are quadrilaterals with opposite sides parallel and all sides are not always equal.

B. Always; parallelograms are quadrilaterals with opposite sides parallel and opposite sides congruent.

C. Never; parallelograms are quadrilaterals with only opposite angles congruent. All sides are not congruent.

Determine and explain whether the statement is sometimes, always, or never true. A square is a parallelogram.

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(over Lesson 10-6)

1. A2. B3. C

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A. Sometimes true; a rhombus is a parallelogram with 4 congruent sides. If a rhombus also has 4 right angles, it is a square.

B. Always true; all four sides and angles of a rhombus are equal.

C. Never true; an angle of a rhombus cannot be 90° whereas an angle of a square is always 90°.

Determine and explain whether the statement is sometimes, always, or never true. A rhombus is a square.

(over Lesson 10-6)

1. A2. B3. C4. D

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A B C D

A. sqaure

B. rectangle

C. trapezoid

D. rhombus

Which of the following is not a parallelogram?

(over Lesson 10-6)

A. AB. BC. CD. D

0% 0%0%0%

A. 6.7 cm

B. 10.6 cm

C. 11.7 cm

D. 43.9 cm

Find the value of x in the pair of similar figures.

(over Lesson 10-7)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. 16.3 ft by 20.1 ft

B. 8.8 ft by 7.1 ft

C. 8.5 ft by 10.5 ft

D. 1.4 ft by 1.7 ft

Caren’s dollhouse furniture is made to scale of real furniturewith a ratio of inch to 1 foot. If a dollhouse table is 3.4inches wide and 4.2 inches long, what are the dimensions ofthe “real” table from which it was modeled?

(over Lesson 10-7)

1. A2. B3. C4. D

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A B C D

A. All squares are similar.

B. All rectangles are similar.

C. All right triangles are similar.

D. All acute triangles are similar.

Which statement is true?

(over Lesson 10-7)

A. AB. BC. CD. D

0% 0%0%0%

A. yes; pentagon; regular

B. yes; pentagon; not regular

C. No; all angles are not equal.

D. No; all sides are not of the same length.

Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why.

(over Lesson 10-8)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. yes; quadrilateral; regular

B. yes; quadrilateral; not regular

C. No; all angles are not equal.

D. No; all sides are not equal.

Determine whether the figure is a polygon. If it is, classify the polygon and state whether it is regular. If it is not a polygon, explain why.

(over Lesson 10-8)

1. A2. B3. C4. D

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A B C D

C. 120

D. 150

Find the measure of an angle in a regular hexagon. Round to the nearest tenth of a degree, if necessary.

(over Lesson 10-8)

A. AB. BC. CD. D

0% 0%0%0%

A. 22.5

C. 150

D. 157.5

Find the measure of an angle in a regular 16-gon. Round to the nearest tenth of a degree, if necessary.

(over Lesson 10-8)

1. A2. B3. C4. D

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A B C D

A. 83.2 in.

B. 41.6 in.

C. 16.2 in.

D. 10.2 in.

What is the perimeter of a 13-gon with each side 3.2 inches long?

(over Lesson 10-8)

1. A2. B3. C4. D

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A B C D

A. square and triangle

B. rectangle and trapezoid

C. trapezoid and square

D. rectangle and triangle

Identify the polygons that are used to create the tessellation.

(over Lesson 10-8)

A. AB. BC. CD. D

0% 0%0%0%

A. A'(2, 0), B'(5, 0), C'(5, 4), D'(2, 4)

B. A'(0, 2), B'(3, 2), C'(3, 4), D'(0, 4)

C. A'(0, 2), B'(3, 2), C'(3, 6), D'(0, 6)

D. A'(2, 0), B'(5, 0), C'(3, 4), D'(0, 4)

Rectangle ABCD has vertices A(0, 0), B(3, 0), C(3, 4), and D(0, 4). Find the vertices of ABCD after a translation 2 units up.

(over Lesson 10-9)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. A'(0, –3), B'(3, –3), C'(3, 1), D'(0, 1)

B. A'(–3, 0), B'(0, 0), C'(0, 4), D'(–3, 4)

C. A'(0, 3), B'(3, 3), C'(3, 7), D'(0, 7)

D. A'(0, –3), B'(7, 0), C'(7, 4), D'(3, 4)

Rectangle ABCD has vertices A(0, 0), B(3, 0), C(3, 4), and D(0, 4). Find the vertices of ABCD after a translation 3 units down.

(over Lesson 10-9)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. A'(4, 0), B'(7, 0), C'(7, 4), D'(4, 4)

B. A'(4, 3), B'(7, 3), C'(7, 7), D'(4, 7)

C. A'(0, 3), B'(3, 3), C'(3, 7), D'(0, 7)

D. A'(3, 4), B'(6, 4), C'(6, 8), D'(3, 8)

Rectangle ABCD has vertices A(0, 0), B(3, 0), C(3, 4), and D(0, 4). Find the vertices of ABCD after a translation 4 units right and 3 units up.

(over Lesson 10-9)

A. AB. BC. CD. D

0% 0%0%0%

A. A'(1, 0), B'(4, 0), C'(4, 4), D'(1, 4)

B. A'(–1, 4), B'(2, 4), C'(2, 8), D'(–1, 8)

C. A'(1, –4), B'(4, –4), C'(4, 0), D'(1, 0)

D. A'(–1, –4), B'(2, –4), C'(2, 0), D'(–1, 0)

Rectangle ABCD has vertices A(0, 0), B(3, 0), C(3, 4), and D(0, 4). Find the vertices of ABCD after a translation 1 unit left and 4 units down.

(over Lesson 10-9)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. A'(3, –2), B'(6, –2), C'(6, 2), D'(3, 2)

B. A'(–2, 3), B'(1, 3), C'(1, 7), D'(–2, 7)

C. A'(3, 2), B'(6, 2), C'(6, 6), D'(3, 6)

D. A'(2, –3), B'(5, –3), C'(5, 1), D'(2, 1)

Rectangle ABCD has vertices A(0, 0), B(3, 0), C(3, 4), and D(0, 4). Find the vertices of ABCD after a translation 3 units right and 2 units down.

(over Lesson 10-9)

1. A2. B3. C4. D

0%0%0%0%

A B C D

A. 2 units left, 1 unit up

B. 1 unit left, 2 units up

C. 2 units right, 1 unit up

D. 1 unit right, 2 units up

Triangle XYZ has vertices X(1, 3), Y(2, 5), and Z(2, 0). If X'Y'Z' has vertices X'(3, 4), Y'(4, 6), and Z'(4, 1), describe the translation.

(over Lesson 10-9)

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