Question

a side - side - side congruent triangle theorem
b side - angle - side congruent triangle theorem
c angle - angle - side congruent triangle theorem
d angle - side - angle congruent triangle theorem
e hypotenuse leg congruent triangle theorem
f not congruent

Explanation:

Step1: Analyze the triangles

We have two right - angled triangles \( \triangle VZW\) and \( \triangle ZWY\). The legs \(VZ = ZY\) (marked with equal signs), \(ZW\) is a common leg (reflexive property: \(ZW=ZW\)), and \(\angle VWZ=\angle ZZY = 90^{\circ}\)

Step2: Apply the congruence theorem

For right - angled triangles, if the hypotenuse and a leg of one right - angled triangle are equal to the hypotenuse and a leg of another right - angled triangle, the triangles are congruent. Here, we have two right - angled triangles (\(\angle VWZ\) and \(\angle ZZY\) are right angles), and we are comparing a leg and the hypotenuse (the non - leg side).

Answer:

E. Hypotenuse Leg Congruent Triangle Theorem