Q In the following figures, the sides AB and BC and the median AD of triangle ABC are respectively - Maths - Triangles

Question

Q 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 triangle PQR Prove that triangle ABC is congruent to
triangle PQR

Amit Shukla · Accepted Answer

Dear Student,
As we know,AD is the median to BC of △ABCtherefore, BD=2BCand, PS is the median to QR of △PQRtherefore, QS=2QRHowever,BC=QR2BC=2QR → BD=QS ---1Now,In △ABD and △PQSAB=PQ givenBD=QS from 1AD=PS giventherefore by SSS congruency rule △AMD≅△PQS and ∠ABD=∠PQS  By CPCTso, ∠ABC=∠PQR ----2Now,In △ABC and △PQR,AB=PQ given∠ABC=∠PQR from 2BC=QR giventherefore,by SAS congruency rule ,△ABC≅△PQR

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Q. 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 triangle PQR. Prove that triangle ABC is congruent to triangle PQR .

Q. 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 triangle PQR. Prove that triangle ABC is congruent to triangle PQR
.