Question

Give Line SV parallels Line TU and Triangle SVX =~ Triangle UTXProve: VUTS is a parallelogramWrite a Paragraph Proof.

Answer 1

Step 1:

In this question, we are given the following:

Step 2:

The details of the proof are as follows:

Since

`\begin{gathered} \bar{SV}\text{ is parallel to} \\ \bar{TU} \end{gathered}`

and

`\text{Triangle SVX }\cong\text{ Triangle UTX}`

Then,

`VX\cong\text{ XT ( by }CPCTC\text{ ) }`

CPCTC means corresponding parts of congruent triangles are congruent

and

`UX\text{ }\cong XS\text{ ( by CPCTC)}`

Thus,

VUTS is a parallelogram since diagonals of a parallelogram bisect each other