Question

prove “if two angles of one triangle are congruent to two angles of a second triangle, the the third angles of the triangles are congruent”.

Answer 1

Assume that,

The two angles of one triangle are congruent to two angles of a second triangle.

To prove: The third angles of the triangles are congruent.

Since, two angles of one triangle are congruent to two angles of a second triangle.

Therefore,

$\begin{gathered} \angle C=\angle F \\ \angle A=\angle D \end{gathered}$

Adding these two we get,

$\begin{gathered} \angle C+\angle A=\angle F+\angle D \\ 180-\angle B=180-\angle E\text{ (Using angle sum property of a triangle)} \end{gathered}$

Cancelling 180 on both sides, we get

$\begin{gathered} \angle B=\angle E \\ \therefore\angle B\cong\angle E \end{gathered}$

Hence, if two angles of one triangle are congruent to two angles of a second triangle, the the third angles of the triangles are congruent.