Question

1. 4% of score

by what rule would these two triangles be congruent?
a asa (angle - side - angle) congruence postulate
b sas (side - angle - side) congruence postulate
c hl (hypotenuse - leg) congruence postulate
d sss (side - side - side) congruence postulate

Explanation:

Step1: Analyze triangle congruence rules

Recall the congruence postulates:

• ASA: Two angles and the included side.
• SAS: Two sides and the included angle.
• HL: Hypotenuse and leg (for right triangles).
• SSS: Three sides.

Step2: Examine the triangles

The triangles are right triangles (right angles marked). They share a common hypotenuse (the diagonal of the parallelogram), and each has a leg of length 5 (marked equal) and the right angle (90°) between the leg and the hypotenuse? Wait, no—wait, looking at the diagram, the two right triangles: one has legs (let's see) – wait, the sides: the marked sides: one side is 5 (leg), the hypotenuse is common, and the right angle. Wait, HL: hypotenuse-leg. Wait, but let's check again. Wait, the triangles: each is a right triangle, they have a common hypotenuse, and one leg (length 5) is equal. So HL (Hypotenuse-Leg) Congruence Postulate? Wait, no—wait the options: C is HL. Wait, but let's re-examine. Wait, the diagram: the two triangles are right triangles, they share the hypotenuse (the diagonal), and one leg (the side of length 5) is equal, and the right angle. Wait, HL 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 triangles are congruent. So here, the hypotenuse is common (so equal), one leg is 5 (equal), and both are right triangles. So the rule is HL (Hypotenuse-Leg) Congruence Postulate, which is option C. Wait, but wait the initial thought—wait let's check the options again. Option C: HL (hypotenuse-leg) Congruence Postulate. So that's the rule here.

Answer:

C. HL (hypotenuse-leg) Congruence Postulate