Question

Which theorems prove that triangles SRP and QRP Are Congruent. Check

all that apply*

A. SSS
B. SAS
C. AAS
D. ASA
E. HL

Answer 1

Given:

The figure.

To find:

The theorems that proves triangles SRP and QRP are congruent.

Solution:

From the given figure, it is clear that in triangle SRP and QRP,

Hypotenuse of triangles :
`PS=PQ` (Given)

Legs of triangles :
`SR=QR` (Given)

Since, hypotenuse and one leg of first triangle is equal to the hypotenuse and corresponding leg of another triangle, therefore, both triangles are congruent by HL postulate of congruence.

`\Delta SRP\cong \Delta QRP` (HL postulate of congruence)

Therefore, the correct option is E .