Question

the hl theorem proves these triangles are congruent. false true

Explanation:

The HL (Hypotenuse - Leg) theorem is used to prove the congruence of right - angled triangles. It states that if the hypotenuse and one leg of a right - triangle are equal to the hypotenuse and one leg of another right - triangle, then the two right - triangles are congruent. In the given figure, we can see that the triangles are right - triangles (since there are right - angle markings, implied by the sides being perpendicular as seen from the diagram) and we have two pairs of equal sides (marked with tick marks). But to use HL, we need a hypotenuse and a leg. However, in this case, the triangles can also be proven congruent by SSS (Side - Side - Side) congruence criterion because all three corresponding sides are equal (the two marked legs and the common hypotenuse). But the key point is that HL can be applied here as well because we have a right - triangle, hypotenuse (common side) and a leg (marked side) equal. Wait, no, actually, let's re - examine. The HL theorem requires that we have two right - triangles, with hypotenuse equal and one leg equal. In the diagram, the two triangles are right - triangles (since the sides are perpendicular, forming right angles), they share the hypotenuse (the diagonal side), and have one leg equal (the marked sides). So HL can be used to prove them congruent. So the statement "The HL theorem proves these triangles are congruent" is True.

Answer:

True