Final answer:
To prove ΔQPT = ΔQRT, we can use the congruence postulate and show that their corresponding sides and angles are congruent. By proving that PS = RS and ∠PSQ = ∠RSQ, we can conclude that ΔQPT = ΔQRT.
Step-by-step explanation:
In order to prove that ΔQPT = ΔQRT, we can use the congruence postulate. Given that PS = RS and ∠PSQ = ∠RSQ, we can show that ΔQPT and ΔQRT are congruent by proving that their corresponding sides and angles are congruent.
Let's start by proving that the corresponding sides are congruent. Since PS = RS, we can deduce that PT = RT (by subtracting PS from both sides of the equation).
Next, we can prove that the corresponding angles are congruent. From the information given, we know that ∠PSQ = ∠RSQ. Since the angles are congruent, we can conclude that ∠QPT = ∠QRT (by subtracting ∠PSQ from both sides of the equation).
Therefore, since the corresponding sides and angles of ΔQPT and ΔQRT are congruent, we can conclude that ΔQPT = ΔQRT.