Question

∠xwy, prove that △vyw ≅ △xyw.
side hk ≅ side i by the reflexive property.
△ghk ≅ △jkh using the triangle congruence theorem.
given (overline{pt}congoverline{rs}) and (∠pqtcong∠rqs), prove that △tpq ≅ △srq.

Explanation:

Step1: Identify the common side

In triangles \( \triangle GHK\) and \( \triangle JKH\), side \(HK\) is common to both triangles. By the Reflexive Property of Congruence, \(HK\cong HK\).

Step2: Determine the congruence theorem

If we assume that we have two sides and the included angle (or other appropriate congruent parts) and the common side \(HK\), for triangles \( \triangle GHK\) and \( \triangle JKH\), the Side - Angle - Side (SAS) Triangle Congruence Theorem (or other applicable theorem depending on the full set of given congruent parts, but with the common side and if other parts like two sides and included angle are congruent) can be used.

Answer:

If we assume the full set of congruent parts (say two sides and the included angle along with the common side \(HK\) by Reflexive Property), \( \triangle GHK\cong\triangle JKH\) using the Side - Angle - Side (SAS) Triangle Congruence Theorem.