Question

if m∠acb = m∠acd = 66° and ad = 10, what is ab? diagram of triangle with right angles at d and b ab = blank submit

Explanation:

Step1: Identify congruent triangles

We have two right triangles, $\triangle ACD$ and $\triangle ACB$. Both are right - angled (since $\angle ADC = \angle ABC=90^{\circ}$), they share the hypotenuse $AC$, and $\angle ACD=\angle ACB = 66^{\circ}$. By the Angle - Angle - Side (AAS) congruence criterion, $\triangle ACD\cong\triangle ACB$.

Step2: Use congruence to find $AB$

If two triangles are congruent, their corresponding sides are equal. In $\triangle ACD$ and $\triangle ACB$, the side $AD$ in $\triangle ACD$ corresponds to the side $AB$ in $\triangle ACB$. Given that $AD = 10$, and since $\triangle ACD\cong\triangle ACB$, we have $AB=AD$.

Answer:

$10$