Question

Are the two triangles formed by drawing perpendicular from vertex to base in an equilateral triangle congruent. Explain with figure.

Answer 1

Yes, the two triangles formed by drawing perpendicular from vertex to base in an equilateral triangle congruent.

In ΔABD and ΔACD

∠1 = ∠2----------------(ABC is an equilateral Δ which means all the ∠ are equal)

AB = AC----------------(ABC is an equilateral Δ)

∠3 = ∠4----------------(In an equilateral Δ, the ⊥ is also the ∠ bisector)

∴ ΔABD≅ΔACD----------------(SAS congruence)