Question

ad is an altitude of an isosceles triangle ABC in which ab = AC. show that 1) ad bisects BC 2)ad bisects angle a ​

Answer 1

Answer:

Step-by-step explanation:

Given: ∆ABC is isosceles with AB=AC and AD is perpendicular to BC.

We need to prove that BD=CD.

In ∆ABD and ∆ACD, we have

AB=AC            (Given)

∠ADB=∠ADC          (Each given equal to 90°)

AD=AD              (Common)

Therefore, by RHS congruence rule, ∆ABD≅∆ACD

Hence, we have BD=CD           (Corresponding parts of congruent triangles are equal).

Solution (ii)

We have proved above that ∆ABD≅∆ACD.

It means that ∠BAD=∠CAD          (Corresponding parts of congruent triangles are equal).

∠BAD=∠CAD means that AD bisects ∠A.

Answer 2

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