Question

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

Answer 1

Prove that

Triangle with equal opposite angles has equal sides.

First, draw a perpendicular line down. (So that two equal angles are in both triangles.)

Now, we can observe that

• A right angle is common.

• A perpendicular line is in both triangles.

• Two triangles have a same angle.

We get two same triangles.

(ASA congruence.)

Hence proved.

Answer 2

Answer:

Step-by-step explanation:

Consider the isosceles triangle  A B C  below.

From the triangle,  A B = A C .

To prove that  ∠ A B C = ∠ A C B , we will construct an angle bisector  

A D  of  ∠ B A C ,

Therefore  ∠ B A D  =  ∠ C A D  by construction.

Now, we have two triangles  △ B A C  and  △ C A D . The two triangles share a common side, side  A D .

From the two triangles: A B = A C  , ∠ B A D ≅ ∠ C A D  and  A D≅A D .

By the use of SAS postulate, we can conclude that the two triangles are congruent. Therefore, by the corresponding angles of congruent triangles, ∠ A B C = ∠ A C B .

Thus, we have proved that the angles opposite to equal sides of a triangle are equal.