Question

which triangle congruence theorem can be used to prove the triangles are congruent?

Explanation:

Step1: Analyze the given information

We have two right - angled triangles \( \triangle DNG\) and \( \triangle PNG\). \(DG = PG\) (given as equal sides), \(GN\) is the common hypotenuse for both right - angled triangles (\(\angle DNG=\angle PNG = 90^{\circ}\)).

Step2: Recall the HL (Hypotenuse - Leg) theorem

The HL (Hypotenuse - Leg) theorem states that if the hypotenuse and a leg of one right - angled triangle are equal to the hypotenuse and a leg of another right - angled triangle, then the two right - angled triangles are congruent.

Answer:

HL (Hypotenuse - Leg)