Question

explain whether the triangles are similar.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of interior angles of a triangle is 180°.

Step2: Find the third angle of \(\triangle ABC\)

Let the third angle of \(\triangle ABC\) be \(\angle A\). Then \(\angle A=180^{\circ}-(88^{\circ} + 42^{\circ})=180^{\circ}-130^{\circ} = 50^{\circ}\).

Step3: Compare angles of the two triangles

In \(\triangle ABC\) and \(\triangle FGH\), \(\angle A = 50^{\circ}=\angle F\), \(\angle C=88^{\circ}=\angle H\), and \(\angle B = 42^{\circ}\). Since two pairs of corresponding angles are equal, by the AA (angle - angle) similarity criterion, the two triangles are similar.

Answer:

The triangles \(\triangle ABC\) and \(\triangle FGH\) are similar because two pairs of corresponding angles are equal (\(\angle A=\angle F = 50^{\circ}\) and \(\angle C=\angle H = 88^{\circ}\)).