Question

GIVEN: SV is parallel to TU and triangle SVX is congruent to triangle UTX

Answer 1

Answer:

Hence it is proved that VUTS is a parallelogram.

Step-by-step explanation:

Since ΔSVX ≅ΔUTX AND SV║TU

In the similar triangles ΔSVX and ΔUTX⇒ ∠TVS =∠UTV and ∠VSU =∠SUT

as they are alternate angles therefore ∠VXS=∠UXT. Since all angles of these triangles are same then sides of these triangles will be of same length.Therefore SV=TU.

Similarly in triangles ΔUXV and ΔSXT

∠VSU=∠SUT (alternate angles) then ∠UST=∠SUV (remaining angles of ∠VST and ∠TUV).

And ∠SVT = ∠UTV then ∠TVU=∠VTS (remaining angles of ∠SVU and ∠UTS)

Since these angles are alternate angles therefore VU║ST.

And we know all angles of ΔUVX are equal to angles of ΔSXT

Therefore sides of these triangles will be equal VU= ST.

Now we can say that sides ST and VU are parallel and equal.

Since all opposite sides of VSTU are equal and parallel to each other therefore VSTU is a parallelogram.