The document discusses two conjectures about angles: 1) A linear pair of angles always sums to 180 degrees. 2) Vertical angles are always congruent (equal in measure). It explains that if you accept the linear pair conjecture, you can use deductive reasoning to prove that the vertical angles conjecture must also be true. The document provides examples applying both conjectures to find missing angle measures.

1. Geometry Warm Up: Pg. 131 # 12 to 15

2. C-1: Linear Pair:
If 2 angles form a linear pair then they add up to
180°
1 2
< 1 + < 2 = 180°

3. C-2: Vertical Angles:
If 2 angles are vertical then, they are congruent
2
1 3
4
<1 ≅< 3 and <2 ≅<4

4. If you accept Linear Pair conjecture then
thru DEDUCTIVE Reasoning-you can prove
that Vertical angles are ≅ .
1
4 2
3
Linear Pair: <1 + <2 = 180° If true then other angles
<2 + <3 = 180° must be ≅ . ΤΗΙΝΚ!
<3 + <4 = 180° <2 = <4 therefore:
<4 + <1 = 180° <1 must = <3 and so on.

5. Note: Protractors will NOT work for these
problems!!
You MUST know the rules to solve!
Try it!
1
52° 2
3
m< 1 = Why?
m< 2 = Why?
m< 3 = Why?
Your perspective matters!!

6. Try this one!!
d
f e
93°
g 50°
m 45° c
42°
k a b
h j