1. 21.1
Objective
Prove and use theorems about the angles formed by parallel lines and a transversal.

2. 21.1
Remember that postulates are statements that are accepted without proof. Since the Corresponding Angles postulate is given as a postulate, it can be used to prove the next three theorems.

3. 21.1

5. 21.1
Find mQRS.
x = 118
Corr. s Post.
mQRS + x = 180°
*Def. of Linear Pair*
mQRS = 180° – x
Subtract x from both sides.
= 180° – 118°
Substitute 118° for x.
= 62°

6. Example 1: Using the Corresponding Angles Postulate
21.1
Example 1: Using the Corresponding Angles Postulate
Find each angle measure.
A. mECF
x = 70
Corr. s Post.
mECF = 70°
B. mDCE
5x = 4x + 22
Corr. s Post.
x = 22
Subtract 4x from both sides.
mDCE = 5x
= 5(22)
Substitute 22 for x.
= 110°

7. 21.1
Example 3
Find each angle measure.
A. mEDG
mEDG = 75°
Alt. Ext. s are
Congruent.
B. mBDG
x – 30° = 75°
Alt. Ext. s are congruent.
x = 105
Add 30 to both sides.
mBDG = 105°

8. D B) m( DEF) E F x – 45 = 30 x = 75 m( DEF) = (x+30)0 = (75+30)0
corresponding angles
x – 45 = 30
subtract x from both sides
x = 75
add 45 to both sides
m( DEF) = (x+30)0
= (75+30)0
= 1050
CONFIDENTIAL

9. R T B) m( TUS) S U 36x = 180 x = 5 m( TUS) = 23(5)0 = 1150 13x0 23x0
Same-side interior angles theorem
36x = 180
Combine like terms
x = 5
divide both sides by 36
m( TUS) = 23(5)0
Substitute 5 for x
= 1150
CONFIDENTIAL

10. Check It Out! Example 2
Find mABD.
2x + 10° = 3x – 15°
Alt. Int. s Thm.
Subtract 2x and add 15 to both sides.
x = 25
mABD = 2(25) + 10 = 60°
Substitute 25 for x.

11. 21.1
Example 4
Find x and y in the diagram.
By the Alternate Interior Angles
Theorem, (5x + 4y)° = 55°.
By the Corresponding Angles Postulate, (5x + 5y)° = 60°.
5x + 5y = 60
–(5x + 4y = 55)
y = 5
Subtract the first equation from the second equation.
Substitute 5 for y in 5x + 5y = 60. Simplify and solve for x.
5x + 5(5) = 60
x = 7, y = 5

12. Check It Out! Example 3
Find the measures of the acute angles in the diagram.
By the Alternate Exterior Angles
Theorem, (25x + 5y)° = 125°.
By the Corresponding Angles Postulate, (25x + 4y)° = 120°.
An acute angle will be 180° – 125°, or 55°.
The other acute angle will be 180° – 120°, or 60°.