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.
Answers
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
Hope it's correct nd helps u
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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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