Question

In the adjoining figure, AB = AC and BD = DC.
Prove that A ADB = AADC and hence show that
(i) ZADB = zADC = 90°. (u) ZBAD = ZCAD.​

Answer 1

Step-by-step explanation:

Since, AB = AC,so ∆ABC is isosceles.

therefore, angle ABC = angle ACB [ since,angles opposite to equal sides ] _____ equation no. 1

given, AB=AC and BD=DC and AD is the bisector of angle BAC

Required to proof: ∆ADB = ∆ADC

THEREFORE, in ∆ ADB and ∆ADC,

AB= AC [given ]

angle ABD = angle ACD [ from equation no. 1]

BD = CD [ given ]

Therefore, ∆ ADB is congruent to ∆ ADC [ by SAS rule ]

Also, angle ADB = angle ADC = 90°

[ since, AD is perpendicular to BC ]

Again, angle BAD = angle CAD [ since, AD bisects angle BAC.

HOPE THIS ANSWER IS HELPFUL FOR YOU THOUGH IT'S A BIT DIFFICULT TO UNDERSTAND !!