Question

Given: CD | AB

Prove: mz1+mz2+ m23 = 180°
Statement
CD | AB
m42 = m24
m23 = m25
m24+ mz1 = m2DCB
m2DCB + m25 = 180°
D
A
2
Reason
Given
DC
4 5
1
_____1_______
Linear Pair Postulate
2
3
B

Answer 1

1. line CD is parallel to line Line AB : Given

2. angle 2 = angle 4 and angle 3 is equal to angle 5 ( alternate interior angles)

3. angle DCB + 5 = 180° ( linear pair postulate)

4. angle 4 + angle 1 + angle 5 = 180°( linear pair postulate)

5. angle 1 + angle 2 + angle 3 = 180° ( substitution property)

The sum of angles on a straight line is 180 and the sum of angles in a triangle is also 180°.

To prove that angle 1 + angle 2 + angle 3 = 180°

1. line CD is parallel to line Line AB : Given

2. angle 2 = angle 4 and angle 3 is equal to angle 5 ( alternate interior angles)

3. angle DCB + 5 = 180° ( linear pair postulate)

4. angle 4 + angle 1 + angle 5 = 180°( linear pair postulate)

since angle 3 = angle 5 and angle 2 = angle 4

5. angle 1 + angle 2 + angle 3 = 180° ( substitution property)