Two sides AB and BC and median AM triangle ABC are respectively equal to sides PQ and QR and median PN of APQR Show that: (i) AABM = APQN (ii) AABC = APQR
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As we know
△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
⇒ ½ BC= 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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