Question

[AB] is a diameter of center C(O, 3cm). M is a point on (C) such that MA=MB. D is the symmetric of A with respect to M.

What is the nature of triangle AMB? Justify.​

Answer 1

Isosceles right triangle.

Explanation:

From the given triangle ABM,

AM ≅ MB [Given]

∠AMB is an angle subtended by the diameter AB.

By theorem, angle subtended by a diameter is always 90°.

m∠AMB = 90°

So the given triangle is a right triangle with two equal sides AM and MB.

Therefore, ΔAMB is an isosceles right triangle.