Question

Given:

Angle PRT and Angle USQ are right angles

PR is congruent to US

PQ is congruent to UT


Prove:

Triangle PTU congruent to Triangle UQP

Answer 1

Answer:

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Answer 2

Given :  Angle PRT and Angle USQ are right angles .  PR = US  & PQ = UT

To find : Triangle PTU congruent to Triangle UQP   ΔPTU  ≅ ΔUQP

Solution:

PR  = US

adding RS in both

PR + RS = US + RS

=> PS  = UR

∠PRT = 90°  => ∠URT = 90°

∠USQ  = 90°   =>  ∠PSQ  = 90°

in Δ PSQ  & Δ URT

PS = UR

∠PSQ = ∠URT = 90°

PQ = TU

Δ PSQ  ≅ Δ URT

=> QS = RT

  PR = SU

hence QS² + SU² = RT² + PR²

=> QU² = PT²  

=> QU = PT

in ΔPTU  & ΔUQP

PT = QU ( shown above)

PU = PU common

TU = PQ   given

Hence ΔPTU  ≅ ΔUQP

QED

Proved

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