Question

5. Prove that the bisector of the base of an isosceles triangle drawn from the vertex meets the base at right angles. of the base.​

Answer 1

Answer:

Given : In the figure attached,

          Triangle ABC is an isosceles triangle.

           AB = AC

          AD is the angle bisector of ∠BAC.

           ∠BAD ≅ ∠CAD

To Prove : BD ≅ CD and ∠ADB ≅ ∠ADC ≅ 90°

Proof : From the ΔABD and ΔACD,

         AB ≅ AC [Given]

         AD is common in both the triangles.

         ∠BAD ≅ ∠CAD [Given]

         By the property of (SAS) of congruence both the triangles ΔABD and ΔACD will be congruent.

         Therefore, ∠ADB ≅ ∠ADC ≅  degrees

         and BD ≅ CD

         Hence proved.

Step-by-step explanation: