Question

AD,BE and CF are altitudes of triangle are equal. Find 2 right angles with RHS criteria.

Please answer with explanation.
I'll mark brainliest.​

Answer 1

Step-by-step explanation:

☛Question:-

AD, BE and CF of triangle ABC are equal. Prove that ABC is an equilateral triangle.

☞Answer:-

Given:-

• AD,BE and CF are altitudes of triangle are equal.

To find:-

• ABC is an equilateral triangle.

Solution:-

In right-angle triangles BCE and CBF, we have,

BC = BC (common hypotenuse);

BE = CF (given).

Hence BCF and CBF are congruent, by RHS theorem. Comparing the triangles, we get ∠B=∠C.

This implies that

AC = AB (sides opposite to equal angles).

Similarly,

AD = BE ⇒∠B =∠A

⇒ AC = BC

✿Together, we get AB = BC = AC or △ABC is equilateral. [hence proved]