Question

In two right triangles PQR and XYZ, side PQ=sideXY, side QR= side YZ.
By which congruent criterion, are the two triangles congruent?​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

△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  

⇒  

2

1

​  

BC=  

2

1

​  

QR ∣ 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