Question

∆ABC is an equilateral triangle. AD bisects angle BAC. Show that ∆ABD is congruent to ∆ACD. Which criteria is used and how??
Please reply fast​

Answer 1

Answer:

Method 1:

When AD is the angle bisector of <BAC

ABC is an isosceles triangle in which AB = AC and AD is the bisector of <BAC.

In triangles ABD and ACD

<B = <C

AB = AC

AD is common.

Therefore triangles ABD and ACD are congruent, and so

<ADB = <ADC = 90 degrees because BCD is a straight line and = 180 degrees.

QED.

Method 2:

When AD is the bisector of BC

ABC is an isosceles triangle in which AB = AC and AD is the bisector of BC.

In triangles ABD and ACD

<B = <C

AB = AC

BD = CD.

Therefore triangles ABD and ACD are congruent, and so

<ADB = <ADC = 90 degrees because BCD is a straight line and = 180 degrees.