Question

given the figure of triangles below with sides and angles as marked. select the additional information that is required in order to prove the triangles are congruent by hypotenuse leg congruency. ( overline{ca} cong overline{xv} ) ( angle w cong angle b ) no additional information is required. ( overline{cb} cong overline{vx} ) ( overline{bc} cong overline{wx} )

Explanation:

Step1: Recall Hypotenuse - Leg (HL) Congruence

HL congruence states that for two right - angled triangles, if the hypotenuse and one leg are congruent, then the triangles are congruent.
In right - angled triangles \( \triangle ABC\) and \( \triangle VWX\) (\(\angle A=\angle V = 90^{\circ}\)), we already know that \(AB = VW\) (given as the marked equal sides).

Step2: Identify the required sides

For HL congruence, we need the hypotenuse of one right - triangle to be congruent to the hypotenuse of the other right - triangle.
The hypotenuse of \( \triangle ABC\) is \(BC\) and the hypotenuse of \( \triangle VWX\) is \(WX\).

Answer:

\(\overline{BC}\cong\overline{WX}\)