Question

Ad is an altitude of an isosceles triangle ABC in which ab= AC show that ad bisects BC and AD bisects <A​

Answer 1

Your Question:

AD is an altitude of an isosceles ∆ABC in which AB = AC. Show that AD bisects BC and AD bisects angle A

Your Answer:

Given:

• ∆ABC is an isosceles triangle.
• Where, AB = AC
• AD is an altitude

To prove:

• BD = CD
• angle BAD = angle CAD (it will show that angle A is bisected.

Proof:

In ∆ADB and ∆ADC

• angle ADC = angle ADB (each 90°)
• AB = AC (given)
• AD = AD (common)

So, ∆ADB and ∆ADC are congruent by RHS Congruency

By CPCT,

• BD = CD
• angle BAD = angle CAD

Hence Proved

Answer 2

Answer:

Given:

∆ABC is an isosceles triangle.

Where, AB = AC

AD is an altitude

To prove:

BD = CD

angle BAD = angle CAD (it will show that angle A is bisected.

Proof:

In ∆ADB and ∆ADC

angle ADC = angle ADB (each 90°)

AB = AC (given)

AD = AD (common)

So, ∆ADB and ∆ADC are congruent by RHS Congruency

By CPCT,

BD = CD

angle BAD = angle CAD

Hence Proved

Step-by-step explanation: