Analytic Geometry | Unit 1: Similarity, Congruence & Proofs Lesson 1 Name ____________________________________________ Date _________________ Period ______ Topic: Reasoning in Algebra and Geometry Class Website: msgiwa1.weebly.com

Analytic Geometry | Unit 1: Similarity, Congruence & Proofs Lesson 1 Topic: Complementary and Supplementary Angles Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name  Class  Date 

Practice Form G

Reasoning in Algebra and Geometry

Fill in the reason that justifies each step.

1. 0.25x + 2x + 12 = 39 Given

2.25x + 12 = 39 a. ?

2.25x = 27 b. ?

225x = 2700 c. ?

x = 12 d. ?

2. Given: m∠ABC = 80

m∠ABD + m∠DBC = m∠ABC Angle Addition Postulate

(3x + 3) + (6x + 5) = 80 Substitution Property

9x + 8 = 80 a. ?

9x = 72 b. ?

x = 8 c. ?

3. Given: KL = 3(PM)

5x = 3(2x - 4) Substitution Property

5x = 6x - 12 a. ?

-x = -12 b. ?

x = 12 c. ?

4. Given: XY = YZ

8m + 5 = 6m + 17 Substitution Property

2m + 5 = 17 a. ?

2m = 12 b. ?

m = 6 c. ?

Name the property of equality or congruence that justifies going from the first statement to the second statement.

5. XY ≅ TZ 6. 3(x + 2) = 15

TZ ≅ XY 3x + 6 = 15

7. 4n + 6 - 2n = 9 8. ∠A ≅ ∠B and ∠B ≅ ∠C

2n + 6 = 9 ∠A ≅ ∠C

CB

A

D(3x 3)

(6x 5)

LK5x

P M2x 4

X Y Z

8m 5 6m 17

Analytic Geometry | Unit 1: Similarity, Congruence & Proofs Lesson 1

TYPES OF ANGLES: Sketch: 1. Acute: Acute angles have measures between _____ and _____.

2. Right: A right angle has measure equal to _____. 3. Obtuse: Obtuse angles have measures between _____ and _____.

SPECIAL PAIRS OF ANGLES: 4. Complementary Angles: Pair of angles whose sum of measures equals _____.

40° and 50° angles are complementary angles because 40° + 50° = 90°. Example: A 40° angle is called the complement of the 50° angle. Similarly, the 50° angle is the complement of the 40° angle.

Practice: Find the complement of each angle.

a) 35° b) 48° c) 12°

5. Supplementary Angles: Pair of angles whose sum of measures equals _____.

60° and 120° angles are supplementary angles because 60° + 120° = 180°. Example: A 60° angle is called the supplement of the 120° angle.

Similarly, the 120° angle is the supplement of the 60° angle. Practice: Find the supplement of each angle.

a) 40° b) 126° c) 72°

1. Angle Bisector: A ray (or line or segment) that divides an angle into two

_____________________________ (two angles with equal measure). Topic: Vertical Angles and Linear Pairs

If two angles share a ___________ and together they make a _______________________, then the two angles are called a linear pair.

 

 

Analytic Geometry | Unit 1: Similarity, Congruence & Proofs Lesson 1 Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name  Class  Date 

Practice Form K

Proving Angles Congruent

Find the value of each variable.

1. To start, identify the relationship between the marked angles in the diagram.

The marked angles are ? .

Then write an equation to express this relationship.

? = ?

2. 3.

Find the measures of the labeled angles in each exercise.

4. Exercise 1 5. Exercise 2 6. Exercise 3

Developing Proof Complete the following proof by filling in the blanks.

7. Given: ∠1 ≅ ∠2

Prove: ∠3 ≅ ∠4

Statements Reasons

1) ∠1 ≅ ∠2

2) m∠1 + m∠3 + m∠5 = 180

3) m∠1 + m∠3 + 90 = 180

4) m∠1 + m∠3 = 90

5) m∠4 + m∠2 = m∠5

6) m∠4 + m∠2 = 90

7) m∠4 + m∠1 = 90

8) m∠4 = m∠3

1) Given

2) ?

3) ?

4) ?

5) ?

6) ?

7) ?

8) ?

8. Reasoning ∠A and ∠B are adjacent complementary angles. ∠C is supplementary to the angle formed by ∠A and ∠B. What can you conclude about ∠C? Explain.

(68 x) 3x

y(10x 18)

(8x 14)

y(3x 10)

(4x 40)

13

2

5

4

Analytic Geometry | Unit 1: Similarity, Congruence & Proofs Lesson 1

Copyright © by Pearson Education, Inc., or its affiliates. All Rights Reserved.

Name  Class  Date 

9. Developing Proof Fill in the blanks to complete the paragraph proof below.

Given: ∠1 ≅ ∠4

Prove: ∠2 ≅ ∠3

∠1 ≅ ∠4 because it is given. ∠1 ≅ ∠2 by the ? . ∠2 ≅ ∠4 by the ? . ∠3 ≅ ∠4 by the ? . It follows that ? ≅ ? by the ? .

Algebra Find the value of each variable and the measure of each labeled angle.

10. 11.

Name two pairs of congruent angles in each figure. Justify your answers.

12. 13.

Algebra Find the measure of each angle.

14. ∠A is three times as large as its complement, ∠B.

15. ∠A is 21 less than twice as large as its supplement, ∠B.

16. ∠A is congruent to its supplement, ∠B.

17. ∠A is 18 more than five times its complement, ∠B.

123

4

(5x 8)

(10x 2)

(9x 2)

(3x 10)

(10x 12)

XQW

Y

ZA

BF

H

E

DG

C

Practice (continued) Form K

Proving Angles Congruent