Question

Use ΔPQR below to answer the question that follows: Triangle PQR with sides PR and QR intersected by segment ST. Which fact is not used to prove that PQR is similar to STR? Segments ST and PQ are parallel. Angle P is congruent to itself due to the reflexive property. RP is a transversal line passing ST and PQ. Angles RTS and RQP are congruent due to the Corresponding Angles Postulate

Answer 1

Answer:The fact '
`\angle P` is congruent to itself due to reflexive property' is not used to prove that
`\triangle PQR\sim \triangle STR`

Explanation:

Here we have a triangle PQR in which ST is the line segment which joins the points S and T where
`S\in PR` and
`T\in QR`

Now let
`ST\parallel PQ`

And, here PR is the common transversal which passes through the parallel lines ST and PQ.

So, In triangles PQR and STR,

`\angle R= \angle R` ( reflexive )

`\angle RTS\cong \angle RQP` ( by corresponding angle postulate)

Thus,
`\triangle PQR\sim \triangle STR` ( by AA postulate of similarity)

Therefore, from the above proof we can say that except the fact '
`\angle P` is congruent to itself' we are using all the given options.