Question

use only ASA congruence theorem and give your solution.​

Answer 1

Answer:

Given

In ABC

AC=15cm

BC=12cm

angle B=90°

In PQR

PQ=9cm

QR=12cm

angle Q=90°

So, In PQR

Applying Pythagoras theorem as it is a right angle triangle.

PR²=PQ²+QR²

PR²= 9²+12²

PR²=81+144

PR²=225

PR=√225

PR=15cm

SIMILARLY,

In ABC

AC²=AB²+BC²

15²=AB²+12²

15²-12²=AB²

AB²=225 - 144

AB²=81

AB=√81

AB=9cm

Both the triangles have all sides equal, so we can say both of them have same angles also, So

angleA=angleP...................1

Now,

In ABC and PQR

Angle B =Angle Q(given,each 90°)

BC=QR(both 12cm)

Angle A=Angle P(from equation 1)

So,

ABC congruent to PQR.

hope it helps..