Question

question 2 of 25

the hl congruence theorem for right triangles is a special case of the ______.

a. sas postulate
b. aas theorem
c. sss postulate
d. asa postulate

Explanation:

Define the HL Congruence Theorem

Using the Triangle Congruence Postulates knowledge point
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 triangles are congruent.

Apply the Pythagorean Theorem to find the third side

Using the Pythagorean Theorem knowledge point

$$
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$$

Since the hypotenuse \(c\) and one leg \(a\) are congruent in both right triangles, the remaining leg \(b\) must also be congruent.

Relate to standard congruence postulates

Using the Triangle Congruence Postulates knowledge point
Since all three pairs of corresponding sides are congruent (the given leg, the hypotenuse, and the calculated third side), the triangles are congruent by the Side-Side-Side (SSS) postulate. Thus, HL is a special case of SSS.

Answer:

• (A) SAS postulate
• (B) AAS theorem
• (C) SSS postulate (Correct answer)
• (D) ASA postulate