Question

statement reason gk || hj a ∠ijh ≅ ∠ikg b ∠i ≅ ∠i c △gik ~ △hij d

Explanation:

Step1: Identify the reason for \(GK\parallel HJ\)

From the diagram, we can see that \(GK\) and \(HJ\) have the same direction arrows, which is a visual indication of parallel lines. So, the reason \(A\) is "Given (from the diagram's arrow markings)".

Step2: Explain \(\angle IJH\cong\angle IKG\)

When two parallel lines (\(GK\parallel HJ\)) are cut by a transversal (\(IK\)), corresponding angles are congruent. So, the reason \(B\) is "Corresponding Angles Postulate".

Step3: Justify \(\angle I\cong\angle I\)

This is the reflexive property of congruence, which states that any angle is congruent to itself. So, the reason \(C\) is "Reflexive Property of Congruence".

Step4: Prove \(\triangle GIK\sim\triangle HIJ\)

Since two angles of \(\triangle GIK\) (\(\angle I\) and \(\angle IKG\)) are congruent to two angles of \(\triangle HIJ\) (\(\angle I\) and \(\angle IJH\)) respectively, by the AA (Angle - Angle) similarity criterion, the triangles are similar. So, the reason \(D\) is "AA (Angle - Angle) Similarity Theorem".

Answer:

A: Given (from the diagram's arrow markings); B: Corresponding Angles Postulate; C: Reflexive Property of Congruence; D: AA (Angle - Angle) Similarity Theorem.