Answer:
Given: QR = QS (by given)
We are to prove: LS = ZR
Proof:
Since QR = QS, by the SAS (Side-Angle-Side) congruence postulate, we know that triangle QRS is congruent to triangle QSZ (both have two equal sides and included angle).
By the AAS (Angle-Angle-Side) congruence postulate, we know that if two angles of one triangle are congruent to two angles of another triangle, and the included side is congruent, then the two triangles are congruent.
Therefore, by using AAS congruence, we can say that triangle QRS is congruent to triangle QSZ.
By the CPCTC (Corresponding parts of congruent triangles are congruent), we know that if two triangles are congruent, then their corresponding sides are congruent.
Therefore, LS is congruent to ZR.
Therefore, we have proved LS = ZR
Note: The above proof uses the properties of congruence of triangles, if the student is not familiar with this, it might be challenging for them.