Question

The figure below shows segments PQ and RS which intersect at point T. Segment PR is parallel to segment SQ.

Which of these facts is used to prove that triangle PTR is similar to triangle QTS

Line segment RT is congruent to line segment TS because corresponding parts of congruent triangles are congruent.

Line segment PR is congruent to line segment SQ because parallel segments are congruent.

Angle PTR is congruent to angle QTS because they are vertical angles.

Angle PRT is congruent to angle QST because they are vertical angles.

Answer 1

Correct answer is C.

It is the only correct statement. All other statements are incorrect.

Answer 2

The correct option is 3.

Explanation:

Given information: Segments PQ and RS which intersect at point T. Segment PR is parallel to segment SQ.

Two triangles are called similar triangles if all the corresponding sides are proportional or all the corresponding angles are congruent.

In triangle PTR and triangle QTS,

`\angle PRT=\angle QST` (Alternate interior angles)

`\angle RPT=\angle SQT` (Alternate interior angles)

`\angle PTR=\angle QTS` (Vertically opposite angles)

By AA rule of similarity,

`\triangle PTR\sim \triangle QTS`

Therefore the fact "Angle PTR is congruent to angle QTS because they are vertical angles" is used to prove that triangle PTR is similar to triangle QTS.

Third option is correct.