Download Geometry Lesson 2-7: Prove Angle Pair Relationships

Geometry
2.7 – Prove Angle Pair Relationships
Learning Target: By the end of today’s lesson we will be able to successfully prove angle pair relationships.
RIGHT ANGLE THEOREM:
All right angles are _________________________.
CONGRUENT SUPPLEMENTS THEOREM:
If two angles are supplementary to the same
angle (or to congruent angles), then they are _________________.
If l and 2 are supplementary and 3 and 2 are supplementary, then _______________.
CONGRUENT COMPLEMENTS THEOREM:
If two angles are complementary to the same
angle (or to congruent angles), then they are ________________.
If 4 and 5 are complementary and 6 and 5 are complementary, then _____________.
LINEAR PAIR THEOREM:
If two angles form a linear pair, then they are _____________________.
l and 2 form a linear pair, so l and 2 are supplementary and m1 + m2 = ______.
VERTICAL ANGLES THEOREM:
Vertical Angles are ____________________.
1)
Given: 1 and 2 are supplements.
1 and 4 are supplements.
m2 = 45°
Prove: m4 = 45°
Statements:
Reasons:
1) 1 and 2 are supplements
1) __________________________________________________
1 and 4 are supplements
2) ____________________________________
2) Congruent Supplements Theorem
3) m 2 = m 4
3) __________________________________________________
4) m2 = 45°
4) __________________________________________________
5) m4 = 45°
5) __________________________________________________
2)
Given: 4 is a right angle.
Prove: 2 and 4 are supplementary.
Statements:
Reasons:
1) 4 is a right angle.
1) __________________________________________________
2) ____________________________________
2) Definition of a Right Angle
3)  2   4
3) __________________________________________________
4) m2 + m4 = 180°
4) __________________________________________________
5) 2 and 4 are supplementary
5) __________________________________________________
3) Use the picture below to find the indicated angle.
a) If m4 = 63°, find m1 = _________ and m2= ____________.
b) If m3 = 121°, find m1= _______, m2=_______, and m4=_________.
4) Write and solve an equation to find x.
Use x to find mAEB.