Given: RS and TV bisect each other at point X. TR and SV are drawn Prove: TR || SV
1 answer:
Answer with Step-by-step explanation:
We are given that
RS and TV bisect each other at point X.
![VX=XT](https://tex.z-dn.net/?f=VX%3DXT)
![SX=XR](https://tex.z-dn.net/?f=SX%3DXR)
We have to prove that TR is parallel to SV.
In triangle TXR and VXS
Reason: Given
![SX=XR](https://tex.z-dn.net/?f=SX%3DXR)
Reason: Given
![\angle TXR=\angle VXS](https://tex.z-dn.net/?f=%5Cangle%20TXR%3D%5Cangle%20VXS)
Reason: Vertical opposite angles
![\triangle TXR\cong \triangle VXS](https://tex.z-dn.net/?f=%5Ctriangle%20TXR%5Ccong%20%5Ctriangle%20VXS)
Reason:SAS Postulate
![\angle TRX=\angle VSX](https://tex.z-dn.net/?f=%5Cangle%20TRX%3D%5Cangle%20VSX)
Reason: CPCT
![TR\parallel SV](https://tex.z-dn.net/?f=TR%5Cparallel%20SV)
Reason: Converse of alternate interior angles theorem
Hence, proved.
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