Question

use the figure to complete the sentence by using the drop-down menus.
∠1 ≅ ∠2 by the select choice, so △abc is similar to △ select choice by the select choice
select choice
aa similarity postulate
vertical angles theorem

Explanation:

Step1: Analyze ∠1 and ∠2

∠1 and ∠2 are vertical angles. By the Vertical Angles Theorem, vertical angles are congruent, so ∠1 ≅ ∠2 by the Vertical Angles Theorem.

Step2: Identify similar triangles

Assuming ∠A ≅ ∠E (from the figure's markings, likely alternate interior angles or given), then with ∠1 ≅ ∠2 (vertical angles), by AA (Angle - Angle) Similarity Postulate, △ABC ~ △EDC (or △E DC, depending on correspondence). Wait, looking at the vertices: A - E, B - D, C - C? Wait, the triangles are △ABC and △EDC? Wait, points: A, B, C and E, D, C. So ∠A and ∠E: if we assume AB || ED (from the figure's structure), then ∠A ≅ ∠E (alternate interior angles). Then with ∠1 ≅ ∠2 (vertical angles), so by AA, △ABC ~ △EDC. But first, ∠1 ≅ ∠2 by Vertical Angles Theorem.

Answer:

First drop - down: Vertical Angles Theorem; Second drop - down: EDC (assuming the triangle is △EDC, with vertices E, D, C); Third drop - down: AA Similarity Postulate.

(Note: The second drop - down's triangle name depends on the correspondence. Since ∠A corresponds to ∠E, ∠1 (at C) corresponds to ∠2 (at C), so the triangles are △ABC and △EDC. So the second drop - down should be EDC, making the triangle △EDC. )