Question

which pair of triangles can be proven congruent using the hypotenuse - leg theorem?
a
b
c
d

Explanation:

Step1: Recall Hypotenuse - Leg Theorem

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

Step2: Analyze each option

• Option A: In the first triangle, the markings show two different lengths (one with two ticks and one with one tick) for the legs. In the second triangle, the markings for the legs are also inconsistent with the first triangle's leg - hypotenuse correspondence.
• Option B: In the first right - triangle, assume the leg with one tick and the hypotenuse (the longest side). In the second right - triangle, we can match the leg with one tick (from the first triangle) and the hypotenuse (by visual inspection of the side lengths in the triangles).
• Option C: The leg markings do not match in a way that would satisfy the HL - Theorem. One triangle has a leg with one tick and the other has a leg with a different marking (when considering the right - angle and the hypotenuse relationship).
• Option D: The leg markings (one with two ticks and one with one tick) do not correspond correctly between the two right - triangles for the HL - Theorem.

Answer:

B.