Download 2.6 Practice with Examples

LESSON
2.6
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 109–116
GOAL
Use angle congruence properties and prove properties about special
pairs of angles
VOCABULARY
Theorem 2.2 Properties of Angle Congruence
Angle congruence is reflexsive, symmetric, and transitive.
Theorem 2.3 Right Angle Congruence Theorem
All right angles are congruent.
Theorem 2.4 Congruent Supplements Theorem
If two angles are supplementary to the same angle (or to congruent
angles) then they are congruent.
Theorem 2.5 Congruent Complements Theorem
If two angles are complentary to the same angle (or to congruent angles)
then the two angles are congruent.
Psotulate 12 Linear Pair Postulate
If two angles form a linear pair, then they are supplementary.
EXAMPLE 1
Chapter 2
Theorem 2.6 Vertical Angles Theorem
Vertical angels are congruent.
Finding Angles
Complete the statement given that mAQG 90.
a. mCQE ?
b. If mBQG 113, then mEQF ?
B
C
A
Q
c. mAQG mEQF mBQC ?
E
G
F
SOLUTION
a. CQE and AQC are vertical angles. By Theorem 2.6, they are con-
gruent. By the definition of congruence, mCQE mAQG, so
mCQE 90.
b. By the Angle Sum Theorem, mBQG mAQG mAQB.
Substituting, you get 113 90 mAQB, so mAQB 23 by
subtracting. Finally, EQF AQB because they are vertical
angles. So, mEQF 23.
c. mAQG mAQB mBQC 180. EQF AQB because
they are vertical angles.
So, mAQG mEQF mBQC 180.
Copyright © McDougal Littell Inc.
All rights reserved.
Geometry
Practice Workbook with Examples
37
LESSON
2.6
CONTINUED
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 109–116
Exercises for Example 1
Complete the statement given that mBQD mCQE 90.
Explain your reasoning.
1. mAQG ?
C
D
B
2. mCQA ?
E
Q
A
F
3. If mCQD 31, then mEQF ?
G
4. If mBQG 125, then mCQF ?
Chapter 2
5. mAQB mGQF mEQG ?
6. If mEQF 38, then mBQC ?
EXAMPLE 2
Finding Angles
Find the measure of each numbered angle,
given that mDBE 26.
C
D
2
A
3
1
4 B5
E
G
F
SOLUTION
CBD and DBE are complementary. So, m1 90 26 64.
ABC and CBE are supplementary. So, m2 180 90 90.
ABG and DBE are vertical angles. So, m3 26.
GBF and CBD are vertical angles. So, m4 64.
EBF and CBE are supplementary. So, m5 180 90 90.
38
Geometry
Practice Workbook with Examples
Copyright © McDougal Littell Inc.
All rights reserved.
LESSON
2.6
CONTINUED
NAME _________________________________________________________ DATE ____________
Practice with Examples
For use with pages 109–116
Exercises for Example 2
Find the measure of each indicated angle.
7. ACD and ACB
D
B
54
C
A
Chapter 2
8. QRT and QRU
T
48
R
Q
U
Copyright © McDougal Littell Inc.
All rights reserved.
Geometry
Practice Workbook with Examples
39