Question

In an isosceles triangle ABC, AB= AC and AD bisects angle A. Prove that BD =CD

Answer 1

Step-by-step explanation:

• Given: Triangle ABC is a isosceles triangle in which AB = AC, AD is the angle bisector of angle A

• To prove: BD = DC

• Proof: In triangle ADB and ADC,

AB = AC ( given / ABC is a isosceles triangle)

angle BAD = angle CAD

( AD is the bisector of angle A)

AD = AD (common)

¤ triangle ADB is congruent to triangle ADC

》BD = DC (CPCT)