Given: SV || TU and SVX = UTX Prove: VUTS is a parallelogram. State the given then use CPCTC to say all their parts match and say what specifically makes it a parallelogram.

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Given: SV || TU and SVX = UTX

Prove: VUTS is a parallelogram.
State the given then use
CPCTC to say all their parts match and say what specifically makes it a parallelogram.

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Thus VUTS proves to be a parallelogram.

Step by step explanation:

Ó ΔSVX ≅ΔUTX AND SV║TU

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

since they are alternate angles ∠VXS = ∠UXT. Since all the angles of these triangles are the same the sides of these triangles will be the same length.

Same in ΔUXV and ΔSXT triangles

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

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

Because these angles are alternate angles, so VU║ST.

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

So the sides of these triangles will be equal to VU = ST.

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

Since all other sides of VSTU are equal and parallel to each other, so VSTU is parallel.