SAT question 1c3d613c (Lines, Angles, and Triangles)

Question

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Triangle $A BC$ and triangle $D EF$ are shown. The relationship between the side lengths of the two triangles is such that $\frac{A B}{D E} = \frac{BC}{EF} = \frac{A C}{D F} = 3$ . If the measure of angle $B A C$ is $2 0^{\circ}$ , what is the measure, in degrees, of angle $E D F$ ?

College Board · Accepted Answer

The correct answer is 20. The correct answer is 20 . By the equality given, the three pairs of corresponding sides of the two triangles are in the same proportion. By the side-side-side (SSS) similarity theorem, triangle ABC is similar to triangle DEF . In similar triangles, the measures of corresponding angles are congruent. Since angle BAC corresponds to angle EDF , these two angles are congruent and their measures are equal. It's given that the measure of angle BAC is 20 ^° , so the measure of angle EDF is also 20 ^° .

CookSAT · Answer

Note: The matching side ratios make the triangles similar, so corresponding angles BAC and EDF have equal measures.

Explanation

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SAT Question 1c3d613c: Lines, Angles, and Triangles answer and explanation with Desmos solution

Explanation

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