Please help me with this proof. I have provided the statements, please help me fill in the reasons.

Question

For this assignment, I need to provide the Converse of the Side-Splitter Theorem. I do not understand how to do this. Please help.

Given:

XR = YS

RQ SQ

Prove:

RS||XY

Statements:

1. XR = YS

RQ SQ

2. XR + RQ = YS+SQ

SQ RQ

3. XQ = YQ

RQ SQ

4.∠Q ≅ ∠Q

5.∇XQY ∼ ∇RQS

6.∠1 ≅ ∠2

7.RS||XY

Reasons:

1. Given
2. 
   
3. 
   
4. 
   
5. 
   
6. 
   
7. 
   

Answer 1

given

addition property of equality

distance measure postulate

reflexive

similar triangles have equal angles

CPCTC

congruent alternate interior angles cause parallel lines