Question

which triangles are congruent to e

Explanation:

Step1: Calculate the third angle of triangle E

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle of triangle E be \(x\). Then \(x + 70^{\circ}+50^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-(70^{\circ}+50^{\circ})=60^{\circ}\).

Step2: Check triangle A

Triangle A has angles \(70^{\circ}\), \(50^{\circ}\) and side \(10\mathrm{cm}\). By ASA (Angle - Side - Angle) congruence criterion (if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent). For triangle E and A, two angles (\(70^{\circ}\), \(50^{\circ}\)) and the side (\(10\mathrm{cm}\)) match.

Step3: Check triangle B

Triangle B has angles \(70^{\circ}\), \(60^{\circ}\) which are not the same as triangle E's angles (\(70^{\circ}\), \(50^{\circ}\)).

Step4: Check triangle C

Triangle C has angles \(70^{\circ}\), \(60^{\circ}\) which are not the same as triangle E's angles (\(70^{\circ}\), \(50^{\circ}\)).

Answer:

A.