Question

prove that the sides opposite to equal angles of a triangle are equal​

Answer 1

Answer:

Step-by-step explanation:

From the given information:

∠

B

A

C

=

∠

B

C

A

And:

A

B

=

B

C

To prove that  

A

B

=

B

C

, we will need to construct an angle bisector  

B

D

to  

∠

A

B

C

. Thus:

∠

A

B

D

=

∠

C

B

D

by construction.

We have two triangles,  

△

A

B

D

and  

△

C

B

D

. For the two triangles, the side  

B

D

is common.

Therefore, using the AAS postulate for congruence, we can say that  

△

A

B

D

≅

△

B

C

D

since  

∠

B

A

C

≅

∠

B

C

A

,  

∠

A

B

D

≅

∠

C

B

D

and  

B

D

≅

B

D

.

Therefore, by the corresponding sides of congruent triangles, we can as well conclude that  

B

A

=

B

C