Question

EXERCISE 6B -
1. Examine the following pair of triangles and state which pair of triangles are
similar. Also, write the similarity relation in symbolic form and state the
similarity criterion.
2.1 cm B D
4.2 cm
А A
E (11)
P
(0)
х
95°
40°
4 cm
5 cm
10 cm
8 cm
95°
40°
R
C с
Z
F​

Answer 1

Answer:

( i )

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.

( iv )

In △MNL and △QPR

∠M=∠Q,

QP

MN

=

QR

ML

=

2

1

∴ By SAS criterion of similarity, △MNL∼△QPR

( v )

In △ABC and △EFD

∠A=∠F,

FD

AB

=

FD

BC

=

2

1

∴ By SAS criterion of similarity, △ABC∼△EFD

( vi )

In △DEF and △PQR

Since, sum of angles of a triangle is 180

o

, Hence, ∠F=30

o

and ∠P=70

o

∠D=∠P,

∠E=∠Q,

∠F=∠R,

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