which triangles are similar to △abc? choose 1 answer: △def only △ghi only both neither
which triangles are similar to △abc? choose 1 answer: △def only △ghi only both neither
Answer
Explanation:
Step1: Recall similarity - angle criterion
Two triangles are similar if their corresponding angles are equal. The sum of angles in a triangle is 180°. In (\triangle ABC), (\angle B = 46^{\circ}), (\angle A=79^{\circ}), then (\angle C=180^{\circ}-46^{\circ}-79^{\circ}=55^{\circ}).
Step2: Analyze (\triangle DEF)
In (\triangle DEF), (\angle E = 51^{\circ}), (\angle D = 62^{\circ}), and (\angle F=180^{\circ}-51^{\circ}-62^{\circ}=67^{\circ}). Since the angles of (\triangle DEF) are not equal to the angles of (\triangle ABC), (\triangle DEF) is not similar to (\triangle ABC).
Step3: Analyze (\triangle GHI)
In (\triangle GHI), (\angle H = 46^{\circ}), (\angle I = 79^{\circ}), then (\angle G=180^{\circ}-46^{\circ}-79^{\circ}=55^{\circ}). The angles of (\triangle GHI) are equal to the angles of (\triangle ABC), so (\triangle GHI) is similar to (\triangle ABC) by the AA (angle - angle) similarity criterion.
Answer:
B. (\triangle GHI) only