Question

Show that the bisector of the Vertical angle of an isosceles triangle bisects the base at right angles.​

Answer 1

Step-by-step explanation:

Let ΔABC be the isoceleus triangle with AB=AC and AD as vertical angle bisector

AB=AC

∠B=∠C

∠BAD=∠CAD

So by ASA criteria the triangles are congruent.

⟹BD=DC

So the bisector of vertical angel bisects the

Answer 2

Answer:

Let ABC be an isosceles triangle in which AB=AC

Let AD be the bisector of vertical angle A and Let AD

meet BC in D

Now, in ∆BAD and ∆CAD , we have

AB = AC

∠BAD = ∠CAD

AD = AD

∆BAD = ∆CAD

BD =CD

and ∠ADB = ∠ADC

but ∠ADB + ∠ADC = 180°

∠ADB = ∠ADC = 90°

AD bisects BC at right angles.

Hence, the bisector of vertical angle of an isosceles triangle bisects the base at right angles.