1. Do Now Find the value of x that will make a parallel to b. (7x – 8)°
62° a b
(44 – 3x)° a b
25°
7x – = 180
7x + 54 = 180
7x = 126
x = 18
44 – 3x + 25 = 180
69 – 3x = 180
-3x = 111
x = -37

2. Prove Basic Geometry Proofs by Direct Proofs
A proof is a logical argument that establishes the truth of a statement. 
Developing Proofs:
Make sure each step in the argument is in proper chronological order in relation to earlier steps. 
Make sure that your argument is clearly developed and that each step is supported by a property, theorem, postulate or definition. 

3. Proving Lines Are Parallel
To prove that two coplanar lines that are cut by a transversal are parallel, prove that any one of the following statements is true:
A pair of alternate interior angles are congruent.
A pair of corresponding angles are congruent.
A pair of interior angles on the same side of the transversal are supplementary.

4. 2) Given: 4 & 5 are supplementary. Prove: g||h
Statements
Reasons
1) Given: 1  2
Prove: m||n
1  2
2  3
1  3
m ||n
Given
Vertical Angles Theorem
Transitive Property of Congruence
Corresponding Angles Converse 1 2 3 m n
Statements
Reasons
2) Given: 4 & 5 are supplementary.
Prove: g||h
4 & 5 are supplementary
5 & 6 are supplementary
4  6
g||h
Given
Linear Pair Postulate
Congruent Supplements Theorem
Alternate Interior Angles Converse h g 4 6 5

5. 3) Given: m1 = 53 m 2 = 127 Prove: j||k Statements Reasons 1 3 2 j
3  1
j||k
Given
Linear Pair Postulate
Substitution Property of Equality
Subtraction Property
Substitution
Definition of Congruent Angles
Corresponding Angles Converse

6. Proving Lines Are Perpendicular
To prove that two intersecting lines or line segments are perpendicular, prove that one of the following is true:
When the two lines or line segments intersect, they form right angles.
When the two lines or line segments intersect, the form congruent adjacent angles.

7. Given: 1  2, 1 & 2 are a linear pair. Prove: g  h
Statements
Reasons
1  2
1 = 2
1 and 2 are a linear pair
1 & 2 are supplementary
m1 + m2 = 180
m1 + m 1 = 180
2(m 1) = 180
m 1 = 90
1 is a right angle
g  h
Given
Definition of congruent angles
Linear Pair Postulate
Definition of Supplementary Angles
Substitution Property of Equality
Distributive Property
Division Property of Equality
Definition of a Right Angle
Definition of Perpendicular Lines