Question

if pq=ps,rq=rs show ∆pqr~∆psr and ∆rqt~∆rst

Answer 1

Given  : PQ = PS , RQ = RS

To Find :  Show that ΔPQR ≅ Δ PSR and ΔRQT ≅ Δ RST

Solution:

Comparing ΔPQR and Δ PSR

PQ = PS   ( given )

RQ = RS   ( given )

PR = PR    ( common)

=> ΔPQR ≅ Δ PSR ( SSS)

QED

Congruent Triangles: corresponding angles and sides are congruent  

=> ∠PRQ = ∠PRS

=> ∠TRQ = ∠TRS  ( ∵ T lies on PR)

Comparing ΔRQT and Δ RST

RT = RT   ( common)

∠TRQ = ∠TRS  ( shown above)

RQ = RS   ( given )

=> ΔRQT ≅ Δ RST    ( SAS)

QED

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Answer 2

Step-by-step explanation:

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