Question

If m∠CAD = 12°, CD = 9, and BC = 9, find m∠CAB.

Question 9 options:

12°

24°

78°

6°

Answer 1

It would be 12 as well

Explanation:

If CD=BC then CAD=CAB.

I hope that helps. Let me know if it is right.

Answer 2

Answer : The value of ∠CAB is, 12°

Step-by-step explanation :

The following combinations of the congruent triangle facts will be sufficient to prove triangles congruent.

The combinations are:

(1) SSS (side-side-side) : If three sides of a triangle are congruent to three sides of another triangle then the triangles are congruent.

(2) SAS (side-angle-side) : If two sides and included angle of a triangle are congruent to another triangle then the triangles are congruent.

(3) ASA (angle-side-angle) : If two angles and included side of a triangle are congruent to another triangle then the triangles are congruent.

(4) RHS (right angle-hypotenuse-side) : If the hypotenuse and leg of one right triangle are congruent to the corresponding parts of another right triangle, the right triangles are congruent.

First we have to prove ΔADC ≅ ΔABC

Prove : ΔADC ≅ ΔABC

As,

Side AB = Side AD (side = 9)

Side AC = Side AC (common side)

∠D = ∠B (90°)

That means, in this two sides and included angle of a triangle are equal to another triangle then the triangles are congruent.

ΔADC ≅ ΔABC (by SAS rule)

And, ∠CAD = ∠CAB (by CPCT)

So, ∠CAD = ∠CAB = 12°