P, Q, R and S are four points on a circle. PTR and QTS are straight lines.

Triangle PTS is an equilateral triangle.

Prove that triangle PQR and

triangle SRQ are congruent.

The answer is below

Step-by-step explanation:

Given that Triangle PTS has all sides with equal lengths, it is considered is an equilateral triangle.

Similarly, with < TPS and <TSP aare both equilateral triangle because they have equal length.

Therefore, ∆ PQS and ∆ SRP are congruent based on side-angle-side theorem.

Similarly, given the fact that their congruent sides of congruent triangles are congruent, both Segment PQ is congruent to segment SR.

Also, Segment PR is congruent to segment SQ as a result of congruent sides of the congruent triangles are congruent.

Lastly, the ∆ PQR and ∆ SRQ are congruent based on the side-side-side theorem.