Question

prove that the bisected of the vertical angle of an isosceles triangle bisected the base right angles​

Answer 1

Answer:

Step-by-step explanation:

Let ΔABC be an isosceles triangle such that AB=BC, and AD be the bisector of the vertical angle ∠A, meeting BC in D

In ΔABD and ΔACD,

AB=AC (given)

∠BAD = ∠CAD ( AD bisects ∠A )

AD = AD (common side)

Therefore, by SAS congruence we have,

ΔABD ≅ ΔACD

∠ACB = ∠ ADC

BD = CD  (corresponding parts of congruent triangles)

But ∠ADB + ∠ADC = 180°  (linear pair)

∴ ∠ADB = ∠ADC = 90°

Hence, AD bisects BC at right angles