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°
