Question

PQR is an isosceles triangle with PQ = PR and PS is one of its altitudes.

i) State the three pairs of equal parts in ∆PQS and ∆PRS. ii) Is ΔPQS ≅ ΔPSR?

If congruent , mention the name of congruence criterion used.

Answer 1

Answer:

We have,

We have,According to given figure.

We have,According to given figure.PQ=PR(giventhat)

We have,According to given figure.PQ=PR(giventhat)QS=SR(Bydefinationofmidpoint)

We have,According to given figure.PQ=PR(giventhat)QS=SR(Bydefinationofmidpoint)PS=PS(Commonline)

We have,According to given figure.PQ=PR(giventhat)QS=SR(Bydefinationofmidpoint)PS=PS(Commonline)Then,

We have,According to given figure.PQ=PR(giventhat)QS=SR(Bydefinationofmidpoint)PS=PS(Commonline)Then,ΔSPQ≅ΔSPR (BY congruency S.S.S.)

We have,According to given figure.PQ=PR(giventhat)QS=SR(Bydefinationofmidpoint)PS=PS(Commonline)Then,ΔSPQ≅ΔSPR (BY congruency S.S.S.)Hence, PS bisects ∠PQR by definition of angle bisector.

Step-by-step explanation:

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Answer 2

Answer:

We have,

According to given figure.

PQ=PR(giventhat)

QS=SR(Bydefinationofmidpoint)

PS=PS(Commonline)

Then,

ΔSPQ≅ΔSPR (BY congruency S.S.S.)

Hence, PS bisects ∠PQR by definition of angle bisector.