Chapter 7

Bell RingerGet out your notebook and prepare to take notes on Chapter 7

List five shapes you see in the classroom

Chapter 7

7.1 - Pairs of Angles (Page 303)Essential Questions:

How do we identify types of angles?

How can identifying types of angles allow us to find relationships among angles?

7.1 cont.Vertical anglesFormed by two intersecting linesAngles opposite one another are CONGRUENTCongruent - have the same measure

Adjacent anglesCommon vertex and common side7.1 cont.Example 1:Name a pair of adjacent angles and a pair of vertical angles in the figure below:

What is the measure of angle HGK?1457.1 cont.Supplementary anglesAngles that add to 180 degrees

Complementary anglesAngles that add to 90 degrees7.1 cont.Example 2:Find the measure of the supplement of the angle IGJ in the following figure:

What does the supplement you found represent in the figure?357.1 cont.Perpendicular linesTwo lines that intersect to form a right angle

7.1 cont.Example 3:In the following figure, if the measure of angle DKH is 73, find the measures of the angles GKJ and JKF:

7317737.1 - ClosureHow do we identify types of angles?

Vertical angles, adjacent anglesHow can identifying types of angles allow us to find relationships among angles?Complementary/supplementary anglesIdentify perpendicular lines7.1 - HomeworkPage 305-306, 2-32 even

Bell Ringer (7.2)Get out yesterdays homework assignment

Get out your notebook and prepare to take notes on Section 7.2

List two sets of parallel lines you see in the classroom

7.2 Angles and Parallel Lines (Page 307)Essential Questions:

What is a transversal?What congruent angles are formed when a transversal intersects two parallel lines?

7.2 cont.Parallel LinesEquidistant at all points

TransversalA line that intersects two or more lines at different points

7.2 cont.Corresponding AnglesLie on same side of the transversalHave corresponding positionsAre congruent ONLY when lines are parallelAlternate Interior AnglesLie within a pair of linesOn opposite sides of the transversalAre congruent ONLY when lines are parallel

AEBFEHGFCDGH7.2 cont.Example 1:Identify each pair of corresponding angles and each pair of alternate interior angles in the following figure:

7.2 cont.Example 2:If p is parallel to q in the following figure, and the measure of angle 3 is 56, find the measure of angle 6.

= 567.2 cont.Example 3:In the figure below, explain how you know ?

Alternate interior angles are congruent, therefore, lines a and b are parallel.7.2 - Closure

What is a transversal?A line that intersects two or more lines at different pointsWhat congruent angles are formed when a transversal intersects two parallel lines?Corresponding anglesAlternate interior angles

7.2 - HomeworkPage 309-310, 2-28 even

Bell Ringer (7.3)Get out yesterdays homework assignment

Get out your notebook and prepare to take notes on Section 7.3

List five polygons you see in the classroom

7.3 Congruent Polygons (Page 312)Essential Questions:

Which parts of congruent figures can be congruent to each other?

What are three ways we can demonstrate that two triangles are congruent?

7.3 cont.Congruent Polygons:Polygons that have the same size and shapeCan be slid, flipped, or turned so that one fits exactly on top of the other

Tick marks and arcs tell you which sides and angles are congruentNOTE: When naming congruent polygons, list corresponding vertices in the same order!! (i.e. ABC DEF)

7.3 cont.

Example 1:In the diagram below, list the congruent parts of the two figures. Then write a congruence statement.7.3 cont.Showing Triangles are Congruent:Use corresponding partsUse the following postulates:

NOTE: Order of angles and sides is important!!

7.3 cont.Example 2:Show that the following pair of triangles are congruent:

AngleSideAngleby7.3 - Closure

Which parts of congruent figures can be congruent to each other?Corresponding angles and sides

What are three ways we can demonstrate that two triangles are congruent?SSS, SAS, ASA

7.3 - HomeworkPage 314-316, 2-28 evenSKIP 22

Bell Ringer (7.4)Get out yesterdays homework assignment

Get out your notebook and prepare to take notes on Section 7.4

Answer the following question:

What two characteristics do congruent polygons have in common?

7.4 Classifying Triangles and Quadrilaterals (Page 318)Essential Question:

How do we classify triangles and quadrilaterals?

7.4 cont.Classifying Triangles:Use angles and sides6 types:

Acute(3 acute angles)

Obtuse(1 obtuse angle)

Right(1 right angle)

Equilateral(3 congruent sides)Isosceles(at least 2 congruent sides)Scalene(no congruent sides)7.4 cont.Example 1:Classify LMN by its sides and angles:

2 congruent sides3 acute anglesisosceles acute triangle7.4 cont.Classifying Quadrilaterals:Use angles and sidesName quadrilaterals by listing vertices in consecutive order

7.4 cont.Example 2:How would you classify the following figure?

Opposite sides are parallelAdjacent sides are not equalParallelogram7.4 - Closure

How do we classify triangles and quadrilaterals?

Triangles angles or congruent sides

Quadrilaterals sides and angles

7.4 - HomeworkPage 320, 2-18 even

Bell RingerGet out yesterdays homework assignment

Think of any clarifying questions you may have about 7.1-7.4

Draw and label a trapezoid that contains a right angle.

Mimio SoftwareMatch the angle pair with the proper name

7.1-7.3 Review (Page 317)

7.4 ReviewClassify the following triangle according to its angles and sides:

A triangles sides are all congruent and its angles all measure 60. Classify the triangle.

Determine the best name for the following quadrilateral:

What is the best name for a figure that has four sides congruent, corresponding angles parallel, and all four angles congruent?

QUIZ TOMORROW!!Sections 7.1-7.4

Homework: Page 346-347, 1-12, SKIP #5

Study:7.1-7.4 HomeworkNotesProblems from todays review

Bell Ringer (7.5)Get out your notebook and prepare to take notes on Section 7.5

Prepare to ask questions about the 7-1-7.4 quiz

7.5 Angles and Polygons (Page 324)Essential Question:

How do we find the interior angle measures of a polygon?

7.5 cont.Application:Art, architecture, tile patterns

Common Polygons:

Polygon NameNumber of SidesTriangle3Quadrilateral4Pentagon5Hexagon6Heptagon7Octagon8Nonagon9Decagon10Dodecagon12

7.5 cont.**Sum of the measures of the interior angles depends on the number of sides in the polygon**

Polygon Angle Sum:For a polygon with n sides, the sum of the measures of the interior angles is as follows:

7.5 cont.Example 1:Find the sum of the measures of the interior angles of an octagon.

Octagon = 8 sides

7.5 cont.Example 2:Find the missing angle measure in the following hexagon:

Hexagon = 6 sides

= sum of angle measures

7.5 cont.Regular Polygons:All sides and angles congruentEquation for angle sum:

7.5 cont.Example 3:A design tile is in the shape of a regular nonagon. Find the measure of each angle.

= 1407.5 - Closure

How do we find the interior angle measures of a polygon?

For a polygon of n sides:

For a regular polygon of n sides:

7.5 - HomeworkPage 326-327, 2-28 even, SKIP 6, 22

Bell Ringer (7.6)Get out yesterdays homework assignment

Get out your notebook and prepare to take notes on Section 7.6

Find the measure of each angle of a regular polygon with 14 sides. Round to the nearest tenth.

DO NOT LOSE THE FORMULA SHEET!!

7.6 Areas of Polygons (Page 328)Essential Question:

How do we find the area of a parallelogram, triangle, and trapezoid?

7.6 cont.Application:Construction Farming Architecture Engineering

Area:Number of square units a figure encloses

7.6 cont.

7.6 cont.Example 1:Find the area of the following triangle:

7.6 cont.

7.6 cont.Example 2:Find the area of the following parallelogram:

7.6 cont.

7.6 cont.Example 3:Find the area of the following trapezoid:

7.6 - Closure

7.6 - HomeworkPage 331, 1-11, 15-17

Bell Ringer (7.7)Get out yesterdays homework assignment

Get out your notebook and prepare to take notes on Section 7.7

Find the area of the following trapezoid:

7.7 Circumference and Area of a Circle (Page 336)Essential Questions:

How do we find the circumference and the area of a circle?

How can we use what we already know about area to find the area of irregular figures?

7.7 cont.Review:RadiusDiameterArea

7.7 cont.

7.7 cont.

7.7 cont.Example 1:Find the circumference and area of a circle with a diameter of 9.2 inches.9.2 in.7.7 cont.Example 2: Find the area of the following figure. Round to the nearest tenth.

7.7 - Closure

7.7 - HomeworkPage 338-3392-22 even, 26-30

Bell Ringer

7.1, 7.2 - Review (Page 346)

7.3, 7.4 - Review (Page 347)

7.5 - Review (Page 347)

7.6, 7.7 - Review (Page 347)

Flatland/Big Bang Theory Clips

TEST TOMORROW!!Sections 7.1-7.7

Homework: Page 348, 1-29

Study:7.1-7.7 HomeworkNotesProblems from todays review