SAT Lines, angles, and triangles Question

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Question 1 · Hard · MathSeptember 2025 Batch 2 · Q12Lines, angles, and triangles · 0 solved

Question graph or diagram from the source SAT PDF.

In the figure, line m is parallel to line n, and lines AE and CD intersect at point B. Which additional piece of information is sufficient to prove that triangle ABC is congruent to triangle EBD?

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Strategy

Look for angle relationships created by parallel lines first, then use the intersecting lines to identify vertical angles. After that, see whether the added fact supplies the missing side needed for a triangle congruence test such as ASA, AAS, SAS, or SSS.

Hints (open one at a time)

Hint 1

Start by marking the angle relationships you get automatically from the parallel lines and the two intersecting transversals.

Hint 2

Then check whether the triangles already have enough equal angles and whether the new information supplies a matching side.

Hint 3

Use the fact that a shared intersection creates vertical angles at B, and ask which added side lets you complete a triangle congruence theorem.

Step-by-step Explanation

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