Question

8. In the following figures, the sides AB and BC
and the median AD of triangle ABC are
respectively equal to the sides PQ and QR
and median PS of the triangle POR. Prove
that triangle ABC and triangle PQR are congruent.
​

Answer 1

To prove:

first prove that, that triangle ABD is congruent to triangle PQS

In ABD nd PQS

AB = PQ — given

BD = QS — given

AD = PS — given

Therefore ABD is congruent to PQS by SSS congruent

Then prove ADC is congruent to PSR

AD = PS given

AC = PR given

DC = SR given

therefore ADC nd PSR are congruent by sss criteria

therefore ABC is congruent to PQR

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Answer 2

Answer

Since, BC=QR, we have

BD=QS and DC=SR     [ D is he midpoint of BC, S is midpoint of  QR]

In ΔABD and ΔPQS

AB=PQ    [Given]

AD=PS    [Given]

BD=QS     [Given:  BC=QR⇒2BC=2QR]

Thus , by side - side - side criterion of co ngruence

we have ΔABD≅ΔPQS

Similarly in ΔABD≅ΔPQS

By Side - Side -Side ariterion  of congruence , we have ΔABC≅ΔPQR

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