Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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Assignment Stamp

1.0 complete definitions on basic terms page

1.1 p. 8-9 # 13-31

1.2 p. 20-22 # 11-16, 18-41

1.3 p. 31-32 # 14-23, 26-31, 34-38

1.4 p. 41-42 # 12-35 (odd), 37-42

1.5 p. 41-42 # 12-35, 37-42

DO NOT LOSE THIS PAGE. This page must be turned in on the day of the test. Ten points will be deducted for each missing homework assignment.

Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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1.0 Basic Terms

Term Definition Supplementary Angles

Complementary Angles

Vertical Angles

Adjacent Angles

Congruence

Similarity

Parallel Lines

Perpendicular Lines

Point

Term Definition Line

Plane

Line Segment

Ray

Collinear Points

Coplanar Points

Linear Pair

Midpoint

Between-ness of points

Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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1.1 Points, Lines, and Planes Notes Example 1:

A. Use the figure to name a line containing point K.

B. Use the figure to name a plane containing point L. Guided Practice 1:

A. Use the figure to name a line containing the point X.

B. Use the figure to name a plane containing point Z. Example 2:

A. Name the geometric shape modeled by a 10 × 12 patio.

B. Name the geometric shape modeled by a button on a table. Guided Practice 2:

A. Name the geometric shape modeled by a colored dot on a map used to mark the location of a city.

B. Name the geometric shape modeled by the ceiling of your classroom. Example 3:

Guided Practice 3: A. Choose the best diagram for the given relationship. Plane D contains line a, line m, and line t, with all three lines intersecting at point Z. Also, point F is on plane D and is not collinear with any of the three given lines. (Draw the picture of your answer.)

Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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Example 3: Guided Practice 3: Example 4: A. How many planes appear in this figure? B. Name three points that are collinear. C. Are points A, B, C, and D coplanar? Explain. Guided Practice 4: A. How many planes appear in this figure? B. Name three points that are collinear. C. Are points X, O, and R coplanar?

Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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1.2 Line Segments and Distance Notes

Example 1: Guided Practice 1: A. Find XZ. Assume that the figure B. Find BD. Assume that the figure is

is not drawn to scale. not drawn to scale.

Example 2:

A. Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3. Guided Practice 2:

A. Find the value of a and XY if Y is between X and Z, XY = 𝟑𝒂, XZ = 𝟓𝒂− 𝟒, and YZ = 𝟏𝟒.

B. Find the value of x and BC if B is between A and C, AC = 𝟒𝒙− 𝟏𝟐, AB = 𝒙, and BC = 𝟐𝒙+ 𝟑. Example 3: Guided Practice 3:

Use the number line to find QR. Use the number line to find AB, BC, and AD.

Example 4 Part 1:

A. Find the distance between E(–4, 1) and F(3, –1).

Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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Guided Practice 4 Part 1: A. Find the distance between B. Find the distance between

A(5, 9) and B(–7, –7). X(–6, –10) and Y(–2, –10)

C. Find the distance between Q(8, 5) and R(–1, 3). Example 4 Part 2: Guided Practice 4 Part 2:

A. Find the distance between E(0, –2) and F(–5, –1). A. Find the distance between A(5, 3) and B(–4, –1).

B. Find the distance between X(–6, –5) and Y(–2, –3). C. Find the distance between Q(7, 5) and R(2, 3).

Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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1.3 Locating Points and Midpoint Notes Example 1:

A. DECORATING Marco places a couch so that its end is perpendicular and 2.5 feet away from the wall. The couch is 90 inches wide. How far is the midpoint of the couch back from the wall in feet?

Guided Practice 1:

A. Use the number line to find the midpoint of AX.

Example 2:

A. Find the coordinates of M, the midpoint of GH, for G(8, −6) and H(−14, 12).

Guided Practice 2:

A. Find the coordinates of M, the midpoint of AB, for A(–3, 4) and B(1, 2).

Example 3:

A. Guided Practice 3:

A. Find the coordinates of C, if B(2, 5) is the midpoint of 𝑨𝑪 and A has coordinates 𝟐,𝟓 .

Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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Example 4: A.

Guided Practice 4:

A. What is the measure of 𝑨𝑪 if B is the B. Find the measure of 𝑷𝑸 if Q is the midpoint of 𝑨𝑪? midpoint of 𝑷𝑹.

Example 5:

A. Find X on BD that is 𝟏𝟒 of the distance from B to D.

𝑩 = −𝟔 and 𝑫 = −𝟐

Guided Practice 5:

A. Find P on NM that is 𝟏𝟑 of the distance from N to M.

𝑵 = −𝟑 and 𝑴 = 𝟐

Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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1.4 Angle Measure Notes

Example 1: A. Name all angles that have B as a vertex.

B. Name the sides of ∠5.

Guided Practice 1: Example 2: Classify each angle as right, acute, or obtuse. Use a protractor to measure the angles to the nearest degree.

A. < 𝑻𝒀𝑽

B. <𝑾𝒀𝑻

C. < 𝑻𝒀𝑼

Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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Guided Practice 2: Classify each angle as right, acute, or obtuse. Use a protractor to measure the angles to the nearest degree. A. ∠CZD B. ∠CZE C. ∠DZX Example 3: INTERIOR DESIGN Wall stickers of standard shapes are often used to provide a stimulating environment for a young child’s room. A five-pointed star sticker is shown with vertices labeled. Find m∠GBH and m∠HCI if ∠GBH ≅ ∠HCI, m∠GBH = 2x + 5, and m∠HCI = 3x – 10. Guided Practice 3: Find m∠BHC and m∠DJE if ∠BHC ≅ ∠DJE, m∠BHC = 4x + 5, and m∠DJE = 3x + 30.

Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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1.5 Angle Relationships Notes

Example 1: A. Name an angle pair that satisfies the

condition two angles that form a linear pair.

B. Name an angle pair that satisfies the condition two acute vertical angles.

Guided Practice 1:

A. Name two adjacent angles whose sum is less than 90.

B. Name two acute vertical angles. Example 2:

A. ALGEBRA Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle.

Guided Practice 2:

A. ALGEBRA Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other.

Example 3:

A. ALGEBRA Find x and y so that KO and HM are perpendicular.

Chapter 1 Tools of Geometry Name: _____________________________ Period: _______

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Guided Practice 3: A.

Example 4: Determine whether each statement can be assumed from the figure below. Explain.

A. m∠VYT = 90.

B. ∠TYW and ∠TYU are supplementary.

C. ∠VYW and ∠TYS are supplementary.

Guided Practice 4:

A. Determine whether the statement m∠XAY = 90 can be assumed from the figure.

B. Determine whether the statement ∠TAU is complementary to ∠UAY can be assumed from the figure.

C. Determine whether the statement ∠UAX is adjacent to ∠UXA can be assumed from the figure.