Answer:
Triangle PTS is an equilateral triangle because all sides are equal lengths.
Angle TPS and angle TSP are equal because it is an equilateral triangle.
Triangle PQS and triangle SRP are congruent because of the side-angle-side theorem.
Segment PQ is congruent to segment SR because congruent sides of congruent triangles are congruent.
Segment PR is congruent to segment SQ because congruent sides of congruent triangles are congruent.
Triangle PQR and triangle SRQ are congruent because of the side-side-side theorem.
Δ PQR and Δ SRQ are congruent By SSS rule .
If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
Two triangles are said to be congruent if they are of the same size and same shape. There are 5 conditions for two triangles to be congruent. They are SSS, SAS, ASA, AAS, and RHS congruence properties.
According to the question
P, Q, R and S are four points on a circle.
PTR and QTS are straight lines.
Triangle PTS is an equilateral triangle.
In ΔPTS ,
∠PTS = ∠TPS = ∠TSP = 60°
PT = PS = ST
In ΔPQS and ΔSRP
PS = SP (common side of triangle )
∠QSP = ∠RPS = 60°
∠PQS = ∠SRP ( Angles between same base and parallels are equal)
Therefore,
ΔPQS ≅ ΔSRP (ASA rule)
PTR = QTS (by CPCT)
PQ = SR (by CPCT)
∠QPS = ∠RSP (by CPCT)
Now , in Δ PQR and Δ SRQ
PQ = SR (proved above )
QR = QR (common side )
PR = QS (proved above )
Therefore, Δ PQR ≅ Δ SRQ (By SSS rule)
Hence, Δ PQR and Δ SRQ are congruent By SSS rule .
To know more about Congruence in Triangles here:
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