SOLUTION: I need help with this proof Given: Point P is not a point on line ABCD and PB equals PC Prove: angle ABP is congruent to angle DCP

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Question 178170: I need help with this proof
Given: Point P is not a point on line ABCD and PB equals PC
Prove: angle ABP is congruent to angle DCP
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!

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          statement                     reason
***************************************************************************

1. PB = PC                              1. Given
   line ABCD
   Point P

2. angle PBC congruent anglePCB         2. Base Angle theorem**

3. line ABCD =180 degrees               3. def of a line

4. angle ABP + angle PBC=180            4. partition postulate
   angle DCP + angle PCB=180

5. angle ABP + angle PCB=180            5.subtitution (statement #2)

6. angle ABP + angle PCB=               6. transitive post.
   angle DCP + angle PCB

7. angle ABP + angle DCP                7. subtraction post.

**Base angle theorem states:if two sides of a triangle are congruent, the angles opposite these sides are congruent
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