Is PQS congruent to RQS by HL? If so, name the legs that allow the use of HL.

The Hypotenuse-Leg Congruence Theorem states that when the hypotenuse and one leg of a Right-angled triangle are congruent to that of another Right-angled triangle, the two Right-angled triangles are therefore congruent.

In the diagram given, the hypotenuse (RS) and a leg (QS), of ∆RQS is congruent to the hypotenuse (PS) and a leg (QS) of ∆PQS. Therefore, ∆PQS is congruent to ∆RQS by HL Congruence Theorem.

nishantwork777 nishantwork777 · Answer 2 · 2021-10-15T14:02:39+02:00

Yes, PQS congruent to RQS by HL is true statement according to the diagram.

Hence :

RS ≅ PS

QS ≅ QS

Step-by-step explanation:

Given information:

The hypotenuse RS and PS

And leg QS.

Hypotenuse-Leg (HL) theorem:

The H-L theorem states that If, the hypotenuse and one leg of a Right-angle triangle are congruent to that of another right angle triangle then the given two right angled triangle will be congruent.

As, we can see in the given diagram the hypotenuse (RS) and the leg (QS) of triangle ΔRQS is congruent to hypotenuse (PS) and leg (QS) of triangle ΔPQS.

Hence , we can say that the ΔPQS is congruent to ΔRQS by H-L Congruent theorem.

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