Question

If two sides of a triangle are congruent then the angles opposite to them are

congruent. Prove it if correct I will mark u brainliest​

Answer 1

Given :

Two sides of a triangle are congruent

To Prove :

The angles opposite to the two sides are congruent.

Proof :

Let the two sides AC and BC and angle opposite to them be ∠A and ∠B.

Let D be the midpoint of AB

Join C and D

Since D is the midpoint of AB

$\sf \implies AD ≅ BD$

We have,

CD ≅ CD (common)

It is given that AC ≅ BC

Therefore, by SSS,

ΔACD ≅ ΔBCD

By CPCT,

∠A ≅ ∠B

Hence, proved!

Answer 2

Answer:

Proved: The angles opposite to them are  congruent If two sides of a triangle are congruent.

Step-by-step explanation:

As per the given information, we assume a triangle $ABC$ with two sides congruent named $AC$ and $AB$. As shown in the figure in the attached image.

Where $D$ is the midpoint on the line $BC$,

Now, the angle opposite to the side $AB$ be ∠$C$ and the angle opposite to the side $AC$ be ∠$B$.

With the help of the midpoint $D$, now we have two triangles named Δ$ABD$ and Δ$ACD$.

Now, we have a common perpendicular named $AD$ in both the triangles.

And we already have two sides congruent named $AC$ and $AB$.

As the perpendicular $AD$ divides  ∠$A$ into two equal parts and the perpendicular remains the same in both tringles Δ$ABD$ and Δ$ACD$.

Now, in the triangle,  $ABD$ we get ∠$B$ = $180-$∠$A-$∠$D$ , and same in the triangle, $ACD$ we get ∠$C$ = $180-$∠$A-$∠$D$.

Thus  ∠$C$ is congruent with ∠$B$ hence proved.