Question

[Maths]

∆ABC is a right angled triangle right angled at B. On side AC, a point D is taken such that AD=DC and AB=BD. Find the measure of <CAB.
_____
• Attachment Answers will not be accepted.
• Try to give Step-by-Step Explaination..
• Stars/Mods Pls help!!​

Answer 1

Answer:

Explanation:

Given :

• ∆ABC is a right angled triangle right angled at B.
• AD = DC & AB = BD.

To Find :

• The measure of ∠CAB.

Solution :

Given that, ΔABC is a right angled Δ right angled at B.

=> ∠ABC = 90°

Point D is midpoint of AC such that, AD = DC.

We know that,

In a right angled triangle the midpoint of hypotenuse is its the circumcircle.

=> AB = BD = AD = DC (Circumradii)______(1)

In ΔABD,

=> AB = BD = AD ___[ From eqn. (1) ]

=> ΔABD is a equilateral triangle.

=> ∠A = 60° (Angle of equilateral Δ)

=> ∠CAB = 60°

Hence :

The measure of ∠CAB is 60°.

Answer 2

Given :-

• ΔABC is a right angled triangle and right angled at B

• AD = DC

• AB = BD

To Find :-

• ΔCAB = ?

Solution :-

Here,

As we observed that,

D is taken in such a way that,

AD = DC

AB = BD .... ( 1 )

But,

Here, In the figure,

It is also observed that ,

D is the midpoint of triangle ΔABC

Therefore,

AD = DC = BD

If ,

AD = BD

From ( 1 ) ,

AB = AD

Therefore,

AB = BD = AD

Hence, ΔABD is a equilateral triangle

Now,

As we know that ,

All angles of equilateral triangle are 60°

Therefore,

ΔA = 60°

Thus,

ΔCAB = 60°

Hence , The measure of ΔCAB = 60° $.$