Question

problem 4: (first taught in lesson 30)
complete this sentence with the best of the choices given.
if two angles of a triangle are congruent to two angles of another triangle, then the remaining pair of angles is ________.

Explanation:

Step1: Recall the triangle angle - sum property

The sum of the interior angles of a triangle is \(180^{\circ}\). Let \(\triangle ABC\) and \(\triangle DEF\) be two triangles. If \(\angle A=\angle D\) and \(\angle B = \angle E\), then for \(\triangle ABC\), \(\angle A+\angle B+\angle C=180^{\circ}\), and for \(\triangle DEF\), \(\angle D+\angle E+\angle F = 180^{\circ}\).

Step2: Substitute the equal angles

Since \(\angle A=\angle D\) and \(\angle B=\angle E\), we can substitute into the equations: \(\angle D+\angle E+\angle C=180^{\circ}\) (from \(\triangle ABC\) substitution) and \(\angle D+\angle E+\angle F=180^{\circ}\) (from \(\triangle DEF\)).

Step3: Use the subtraction property of equality

Subtract \((\angle D+\angle E)\) from both equations. We get \(\angle C=180^{\circ}-(\angle D + \angle E)\) and \(\angle F=180^{\circ}-(\angle D+\angle E)\). So \(\angle C=\angle F\).

Answer:

congruent