Question

Given: RS and TV bisect each other at point X. TR and SV are drawn Prove: TR || SV

Answer 1

Answer with Step-by-step explanation:

We are given that

RS and TV bisect each other at point X.

$VX=XT$

$SX=XR$

We have to prove that TR is parallel to SV.

In triangle TXR and VXS

$VX=XT$

Reason: Given

$SX=XR$

Reason: Given

$\angle TXR=\angle VXS$

Reason: Vertical opposite angles

$\triangle TXR\cong \triangle VXS$

Reason:SAS Postulate

$\angle TRX=\angle VSX$

Reason: CPCT

$TR\parallel SV$

Reason: Converse of alternate interior angles theorem

Hence, proved.