Question

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

Answer 1

Explanation:

Given that RS and TV bisect each other at point X

Join RT and VS

Now we have two triangles RXT and VXS with a common vertex X

Compare these two triangles

RS=XS (mid point since bisect)

TX=XV (mid point)

Angle RXT = Angle VXS (vertically opposite angles)

Hence by SAS postulate the two triangles are congruent

Corresponding angles would be equal

i.e. angle RTV = Angle TVS

Since alternate angles made by a transversal are equal

TR is parallel to SV