2.7 – Prove Angle Pair Relationships

2.7 – Prove Angle Pair Relationships

Right Angles Congruence Theorem:

All _____________ angles are ______________ .right congruent

Linear Pair Postulate:

If two angles form a __________ _________,

then they are ____________________.

linear pair

supplementary

Congruent Supplements Theeorem:

If two angles are ______________ to the same

angle, then they are ____________ .congruent

supplementary

123m1 + m2 = 180°

m2 + m3 = 180°

1 3

Congruent Complements Theorem:

If two angles are ______________________ to

the same angle, then they are ___________ .

complementary

congruent

Vertical Angles Congruence Theorem:

Vertical angles are ________________.congruent

1. If m1 = 53°, find m2, m3, m4, and m5.

53°

53° 37°

37°

90°

2. If m4 + m3 = 144°, find m1, m2, and m5.

36°

36°54°

144°

3x + 48 = 180 -48 -48

3x = 1323 3x = 44°

3. Find the value of x.

6x – 2 + 7x = 180

+2 +213x = 18213 13x = 14°

13x – 2 = 180

3. Find the value of x.

8x = 808 8

x = 10°

3. Find the value of x.

9x + 7 = 5x + 67-5x -5x .

4x + 7 = 67

4 4

x = 15°

-7 -74x = 60

3. Find the value of x.

4. Find the value of x and y. Then find the measure of each angle.

4y + 17y – 9 = 180 21x – 3 + 5x + 1 =180

21y – 9 = 180

21y = 189

y = 9

26x – 2 = 180

26x = 182x = 7

4(9) = 36°

36°

144°

36°144°

4. Find the value of x and y. Then find the measure of each angle.

3x + 7 = 4x – 18 7y = 5y + 28 7 = x – 18

25 = x y = 14

7(14) = 98°

2y = 28

82° 98°

82°98°

HW Problem

2.7 # 37

HW ProblemSection Page # Assignment

2.7Ch 2 Review

127-131134-137

138

10-14 even, 28, 376-10, 12-14, 17-20, 225, 9, 10, 17-19

1. Given

2. Def. of comp. angles

m1+m2 = m1+m3 m2 = m3

5. Def. congruent angles