Download Section 2-5: Proving Angles Congruent

Geometry Section 2-5: Proving Angles Congruent
Name:_____________
Date:_____ Period:__
Target Goals:
 I will be able to continue to practice proofs (both two column and paragraph)
 I will be able to apply theorems about congruent angles in proofs
Review from yesterday….
Given: TA is the angle bisector
Solve for x and justify each step
Step
Justification
PART ONE: Complete each definition and draw a picture to represent it.
Vertical Angles are ____________angles whose sides form two pairs of opposite __________.
Picture:
Complimentary Angles are two angles where the _________ of their measures is 90.
Picture:
Supplementary Angles are two angles where the _________ of their measures is 180.
Picture:
**NOTE** We also refer to supplementary angles as a ________________ _____________.
PART TWO:
Example 1: Solve for x
(2x + 3)
(4x – 101)˚
Did you get 52? If so, how did you know that the two expressions were equal? How do we truly
know that vertical angles are congruent?
Vertical Angle Theorem:
Let’s prove this….
Given: < 1 and < 2 are vertical angles
Prove: < 1 and < 2 are congruent
3
1
2
Example 2: Solve for y.
o
o
(6y – 10) (6y + 10)
Did you get y = 15? If so, how did you know to add the given expressions and set them equal to
180°? How do we truly know that any linear pair adds to 180°?
Congruent Supplements Theorem:
Let’s prove this…
Given: <1 and <2 are supplementary
<3 and <2 are supplementary
Prove: <1
 <3
1
2
3
Example 3: Solve for x.
Did you get x = 6? If so, how did you know to add the given expressions and set them equal to
90°? How do we truly know these angles should add to 90°?
Congruent Compliments Theorem:
Let’s prove this…
Given: <1 and <2 are complimentary
<3 and <2 are complimentary
Prove: <1  <3
Other things you should know…
All right angles are:___________________________
If two angles are congruent and supplementary, then each angle must be _______________.
Example 4:  A and  B are complementary angles. Find m  A and m  B if  A is 2 times as
large as its complement.
You try!  A and  B are supplementary angles. Find m  A and m  B if  A is 3 times as large
as its supplement.