Question

I’m going to need you guys to come in clutch. I’m in study hall and have 21 minutes left ( I still need to finish my essay) . You can do come on BRAINLY DONT LET ME DOWN

Answer 1

Step-by-step explanation:

For the given figure PQRS:

Given:

$PS\perp SQ$    

$RQ\perp QS$

$PQ\cong RS$

To prove

$\triangle PSQ\cong \triangle RQS$

In Δ PSQ and ΔRQS

$PS\perp SQ$                             [Given]

$\angle PSQ=90\°$                     [Definition of perpendicular lines]

$\triangle PSQ$ is a right triangle      [Definition of right triangles]

$RQ\perp QS$                             [Given]

$\angle RQS=90\°$                     [Definition of perpendicular lines]

$\triangle RQS$ is a right triangle      [Definition of right triangles]

$PQ\cong RS$                   [Given hypotenuse of both triangles congruent]

$SQ\cong QS$     [ By reflexive property of congruence side QS

                              congruent to itself ]

$\triangle PSQ\cong \triangle RQS$     [H.L. congruence postulate]

Thus triangles are are congruent by Hypotenuse Leg postulate.