Answer with Step-by-step explanation:
We are given that
RS and TV bisect each other at point X.
[tex]VX=XT[/tex]
[tex]SX=XR[/tex]
We have to prove that TR is parallel to SV.
In triangle TXR and VXS
[tex]VX=XT[/tex]
Reason: Given
[tex]SX=XR[/tex]
Reason: Given
[tex]\angle TXR=\angle VXS[/tex]
Reason: Vertical opposite angles
[tex]\triangle TXR\cong \triangle VXS[/tex]
Reason:SAS Postulate
[tex]\angle TRX=\angle VSX[/tex]
Reason: CPCT
[tex]TR\parallel SV[/tex]
Reason: Converse of alternate interior angles theorem
Hence, proved.
