Question

Prove that the bisector of the top angle of an isosceles triangle bisects the base at right angles

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

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 ≅ $\frac{180}{2}=90$ degrees

          and BD ≅ CD

          Hence proved.

Learn more about the properties of an isosceles triangle from https://brainly.in/question/2124472