SAT Lines, angles, and triangles Question

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Question 1 · Hard · MathMay 2024 · Q22Lines, angles, and triangles · 0 solved

In triangle ABC and triangle DEF, sides AB and DE each have a side length of 6 inches, and angles A and D each have an angle measure of $4 0^{\circ}$ . Which of the following additional pieces of information is (are) sufficient to prove whether triangle ABC is congruent to triangle DEF? I. The measures of angles B and C are equal. II. The lengths of sides AC and DF are equal. III. The lengths of sides BC and EF are equal.

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Strategy

Look for a congruence theorem you can actually complete: SAS, ASA, AAS, SSS, or HL. A single matching angle plus one matching side is usually not enough unless the new information supplies the missing side or angle in the right place.

Hints (open one at a time)

Hint 1

You already have one equal side and one equal angle in each triangle. Ask which extra fact would let you use a congruence theorem.

Hint 2

Try checking whether the new information gives you a second matching side that makes the given angle the included angle.

Hint 3

One choice gives you two sides with the known angle between them, which is enough to prove the triangles congruent. The others do not connect the two triangles tightly enough.

Step-by-step Explanation

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