Question

can the hl congruence theorem be used to prove the triangles congruent? if so, write a congruence statement.

Explanation:

Step1: Recall the HL Congruence Theorem

The HL (Hypotenuse - Leg) Congruence Theorem states that if the hypotenuse and a leg of one right - triangle are congruent to the hypotenuse and a leg of another right - triangle, then the two right - triangles are congruent.
In \(\triangle CBA\) and \(\triangle WXY\), \(\angle B=\angle X = 90^{\circ}\) (right angles). The hypotenuse \(AC = WY=13\) and the leg \(AB = WX = 5\).

Step2: Check the congruence statement

For congruent triangles, the order of the vertices matters. In \(\triangle CBA\) and \(\triangle WXY\), when we use the HL theorem, the correspondence of vertices should be such that the right angles, the hypotenuses, and the legs match.
We have \(CB\) corresponding to \(XY\) (not directly used in the HL naming for the congruence statement in terms of vertex order based on hypotenuse - leg), \(BA\) corresponding to \(XW\), and \(AC\) corresponding to \(YW\). The congruence statement \(\triangle CBA\cong\triangle WXY\) follows the vertex - to - vertex correspondence based on the equal hypotenuse and leg.

Answer:

Yes, \(\triangle CBA\cong\triangle WXY\)