Question

In △DEF, ∠D = 64°, ∠F = 75°, DF = 5cm and in △PQR ∠P = 41° ∠Q = 64°, and QR = 5cm. Show

with appropriate steps if the given triangles are congruent. Write the names of the triangles in

symbolic form; also mention the criteria used.​

Answer 1

Answer:

In △ABC and △PQR

∠A=∠P,

∠B=∠Q,

∠C=∠R,

∴ By AAA criterion of similarity, △ABC∼△PQR

( ii )

In △ABC and △QRP

QR

AB

=

RP

BC

=

QP

AC

=

2

1

∴ By SSS criterion of similarity, △ABC∼△QRP

( iii )

In △LMP and △DEF

DE

LM

=

4

2.7

,

DF

LP

=

2

1

The sides are not in the equal ratios, Hence the two triangles are not similar.