Question

1. which statement is true? a) ∠e≅∠f b) ∠g≅∠d c) ∠c≅∠a d) ∠a≅∠h

Explanation:

Step1: Recall angle - pair relationships

When two lines are cut by a transversal, vertical angles are congruent. Adjacent angles are supplementary (add up to 180°) unless they are right - angles. Corresponding angles, alternate interior angles, and alternate exterior angles have specific congruence relationships when the lines are parallel.

Step2: Analyze each option

• Option A: ∠E and ∠F are adjacent angles. They are supplementary (∠E+∠F = 180°) and not congruent in general.
• Option B: ∠G and ∠D are alternate exterior angles. When the two horizontal lines are parallel, alternate exterior angles are congruent.
• Option C: ∠C and ∠A are adjacent angles. They are supplementary (∠C + ∠A=180°) and not congruent in general.
• Option D: ∠A and ∠H are not related by any of the special angle - pair relationships (corresponding, alternate interior, alternate exterior, vertical) and are not congruent in general.

Answer:

B. ∠G≅∠D