Question

from the diagram, what can you conclude about \\(\triangle cad\\)?
it is an isosceles triangle.
it is an equiangular triangle.
it is an obtuse triangle.
it is an equilateral triangle.

Explanation:

Step1: Identify congruent triangles

In right - triangles $\triangle ABC$ and $\triangle AED$, we have $BC = ED$ (marked with double - bars) and $\angle B=\angle E = 90^{\circ}$, $AB = AE$ (marked with single - bars). By the Side - Angle - Side (SAS) congruence criterion, $\triangle ABC\cong\triangle AED$. So, $AC = AD$.

Step2: Recall triangle definitions

An isosceles triangle is a triangle with at least two sides of equal length. Since $AC = AD$ in $\triangle CAD$, $\triangle CAD$ is an isosceles triangle.

Answer:

It is an isosceles triangle.