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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

Im going to need you guys to come in clutch Im in study hall and have 21 minutes left I still need to finish my essay You can do come on BRAINLY DONT LET ME DOW class=

Respuesta :

Step-by-step explanation:

For the given figure PQRS:

Given:

[tex]PS\perp SQ[/tex]    

[tex]RQ\perp QS[/tex]

[tex]PQ\cong RS[/tex]

To prove

[tex]\triangle PSQ\cong \triangle RQS[/tex]

In Δ PSQ and ΔRQS

[tex]PS\perp SQ[/tex]                             [Given]

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

[tex]\triangle PSQ[/tex] is a right triangle      [Definition of right triangles]

[tex]RQ\perp QS[/tex]                             [Given]

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

[tex]\triangle RQS[/tex] is a right triangle      [Definition of right triangles]

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

[tex]SQ\cong QS[/tex]     [ By reflexive property of congruence side QS

                              congruent to itself ]

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

Thus triangles are are congruent by Hypotenuse Leg postulate.

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