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3. Two sides AB and BC and median AMof one triangleABC are respectively equal to sides PQ and QR andmedian PN of ΔPOR. Show that:(i) ΔΑΒΜ = ΔΡQΝ(ii) ΔABC = ΔPQR |
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Answer» △ABC and△PQR in which AB=PQ,BC=QR and AM=PN. Since AM and PN are MEDIAN of triangles ABC and PQR respectively. Now, BC=QR ∣ Given ⇒½BC = ½QR ∣ Median divides opposite SIDES in TWO equal parts BM=QN... (1) Now, in △ABM and△PQN we have AB=PQ ∣ Given BM=QN ∣ From (i) and AM=PN ∣ Given ∴ By SSS criterion of congruence, we have △ABM≅△PQN, which proves (i) ∠B=∠Q ... (2) ∣ Since, corresponding parts of the congruent triangle are equal Now, in △ABC and△PQR we have AB=PQ ∣ Given ∠B=∠Q ∣ From (2) BC=QR ∣ Given ∴ by SAS criterion of congruence, we have △ABC≅△PQR, which proves (ii) |
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