2 sides AB and BC and the median AM of triangle ABC are respectively equal to side DE and EF and the median DN of triangle DEF .Prove that triangle ABC congruent to triangle DEF.
Share
2 sides AB and BC and the median AM of triangle ABC are respectively equal to side DE and EF and the median DN of triangle DEF .Prove that triangle ABC congruent to triangle DEF.
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
△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
⇒21BC=21QR ∣ 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)