Question

are these triangles similar? i j k g h yes no

Explanation:

Step1: Identify the shared angle

Triangles \( \triangle IKH \) and \( \triangle JKG \) share \( \angle K \), so \( \angle IKH = \angle JKG \).

Step2: Check parallel lines and corresponding angles

The marked segments (with arrows) indicate \( JG \parallel IH \) (since the arrows show the lines are parallel). By the Basic Proportionality Theorem (Thales' theorem) or the AA (Angle - Angle) similarity criterion, since \( \angle IKH=\angle JKG \) (common angle) and \( \angle I=\angle J \) (corresponding angles from parallel lines \( JG\parallel IH \)), the triangles are similar by AA similarity.

Answer:

yes