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: Identify the triangles' properties

Both triangles are right - angled (right angles at \(Q\) and \(B\)).

Step2: Check the hypotenuse and leg

In right - angled triangles, if the hypotenuse and one leg of one right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle, the triangles are congruent. Here, the hypotenuses (marked with one cross) and one leg (marked with two crosses) are equal.

Answer:

E. Hypotenuse Leg Congruent Triangle Theorem