Question

If one angle of a triangle is equal to one angle of the other triangle and sides including
these angles are proportional, then two triangles are similar.​

Answer 1

Step-by-step explanation:

Construction: Two triangles ABC and DEF are drawn so that one of the angles of one triangle is equal to one of the angles of another triangle. Moreover, two sides included in that angle of one triangle are proportional to two sides included in that angle of another triangle. This means;

∠ A = ∠ D and

A

B

D

E

=

A

C

D

F

theorem on similarity of triangles

To Prove: Δ ABC ∼ Δ DEF

Draw PQ in triangle DEF so that, AB = DP and AC = DF

Proof:

Δ

A

B

C

≅

Δ

D

P

Q

Because corresponding sides of these two triangles are equal

A

B

D

E

=

A

C

D

F

given

∠ A = ∠ D

Hence;

A

B

D

E

=

B

C

E

F

from SSS criterion

Hence;

A

B

D

E

=

A

C

D

F

=

B

C

E

F

Hence; Δ ABC ∼ Δ DEF proved

Answer 2

Answer:

ye wala answer correct hai.