Question

In ∆MNL and ∆PQR, MN = 2cm , PQ = 4cm, NL = 3cm, QR = 6cm,
ML = 5cm, PR = 10cm .


State the similarity criterion by which the triangles are similar.​​

Answer 1

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As in bothe triangles the ratio of corresponding sides will be equal i.e., 1/2

so these triangles will be similar on the basis of SSS similarity rule.

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Answer 2

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

Step-by-step explanation:

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