Question

yes
no
write a similarity statement.
△□ ~ △

Explanation:

Step1: Identify Parallel Lines and Angles

The red arrows indicate that \(JG \parallel IH\) (assuming the markings show parallel segments). So, \(\angle KJG \cong \angle KIH\) (corresponding angles) and \(\angle KGJ \cong \angle KHI\) (corresponding angles). Also, \(\angle K\) is common to both \(\triangle KJG\) and \(\triangle KIH\).

Step2: Apply AA Similarity Criterion

By the Angle - Angle (AA) similarity postulate, if two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. Since \(\angle K\) is common, and we have two pairs of corresponding congruent angles from the parallel lines, \(\triangle KJG \sim \triangle KIH\) (or \(\triangle KGJ \sim \triangle KHI\), but the order of vertices should match the corresponding angles). Looking at the triangle labels, the smaller triangle is \(\triangle KJG\) (with vertices \(K\), \(J\), \(G\)) and the larger one is \(\triangle KIH\) (with vertices \(K\), \(I\), \(H\)). Alternatively, if we consider the other pair, \(\triangle JGH\) and \(\triangle IHH\)? Wait, no. Wait, the segments: \(JG\) and \(IH\) are parallel, and \(KG\) and \(KH\) are on the same line, \(KJ\) and \(KI\) are on the same line. So the similar triangles should be \(\triangle KJG\) and \(\triangle KIH\) (or \(\triangle KGJ\) and \(\triangle KHI\)). But let's check the vertex order. The angle at \(K\) is common, angle at \(J\) corresponds to angle at \(I\), angle at \(G\) corresponds to angle at \(H\). So the similarity statement is \(\triangle KJG \sim \triangle KIH\) (or \(\triangle KGJ \sim \triangle KHI\)). But looking at the triangle with vertices \(K\), \(J\), \(G\) and \(K\), \(I\), \(H\). So the first triangle is \(\triangle KJG\) and the second is \(\triangle KIH\).

Answer:

\(\triangle KJG \sim \triangle KIH\) (or \(\triangle KGJ \sim \triangle KHI\), but the most appropriate based on the diagram's vertex labels is \(\triangle KJG \sim \triangle KIH\))