Question

6. If the corresponding angles of two triangles are equal then prove that the
triangles are similar.

Answer 1

Answer:

Construction: Two triangles ABC and DEF are drawn so that their corresponding sides are proportional. This means:

A

B

D

E

=

A

C

D

F

=

B

C

E

F

To Prove: ∠ A = ∠ D, ∠ B = ∠ E and ∠ C = ∠ F

And hence; Δ ABC ∼ Δ DEF

In triangle DEF, draw a line PQ so that DP = AB and DQ = AC

Proof:

Δ

A

B

C

≅

Δ

D

P

Q

Because corresponding sides of these two triangles are equal

This means;

D

P

P

E

=

D

Q

Q

F

=

P

Q

E

F

This also means; ∠ P = ∠ E and ∠ Q = ∠ F

We have taken; ∠ A = ∠ D, ∠ B = ∠ P and ∠ C = ∠ Q

Hence; ∠ A = ∠ D, ∠ B = ∠ E and ∠ C = ∠ F

From AAA criterion;

Δ ABC ∼ Δ DEF proved