Question

do these triangles satisfy hl theorem?

o obviously not
o clearly they do

Explanation:

Step1: Recall HL Theorem

HL (Hypotenuse - Leg) theorem applies to right - angled triangles. It 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. First, we need to check if the triangles are right - angled. From the diagram, there is no indication that these triangles are right - angled (no right - angle symbol). Also, for HL, we need a hypotenuse (the side opposite the right - angle) and a leg. Since the triangles do not appear to be right - angled, they cannot satisfy the HL theorem. But wait, maybe we misinterpret? Wait, the original thought was wrong. Wait, no, let's re - examine. Wait, the HL theorem requires right triangles. If the triangles are not right - angled, they can't satisfy HL. But also, let's check the markings. The first triangle has a single - marked side, double - marked side, and an angle. The second triangle has double - marked side, single - marked side, and an angle. But HL is for right triangles. Since there's no right - angle, they can't satisfy HL. But the option "obviously not" is a candidate. Wait, but maybe the user made a mistake? Wait, no, the correct analysis: HL needs right triangles. These triangles don't have right - angles (no 90 - degree symbol), so they can't satisfy HL. So the answer should be "obviously not". Wait, but the initial option selected was "clearly they do", which is wrong. So let's correct.

Step2: Analyze Triangle Type and HL Requirements

HL theorem is only applicable to right - angled triangles. The given triangles do not have a right - angle (no right - angle symbol in the diagram). Also, even if we assume they were right - angled, the markings (congruent sides and angles) do not match the HL criteria (hypotenuse and leg congruence). So the triangles do not satisfy the HL theorem.

Answer:

obviously not