Digital SAT® Practice Test 1: Math Module 2 (Hard): Question 11 Explanation

Digital SAT Math Test 6 Question 11

In triangle $ABC$ and $XYZ$, angles $A$ and $X$ each have measure $50°$, $AC=3$, and $XZ=9$. Which additional piece of information is sufficient to prove that triangle ABC is similar to triangle $XYZ$?

$BC=6$ and $YZ=6$
$BC=6$ and $YZ=18$
The measure of angles $B$ and $Y$ are $30°$ and $90°$, respectively.
The measure of angles $B$ and $Z$ are $30°$ and $100°$, respectively.

Answer:

Explanation

The correct answer is Choice D.

When two angles of a triangle are equal to any two angles of the other triangle (AA), two triangles are similar.

Since two angles each of triangles $ABC$ and $XYZ$ are equal, similarity is already established and no additional piece of information is required.

Choices A and B are incorrect because to satisfy SAS similarity, the information on the others side should be $AB$ and $XY$.

Choice C is incorrect because the given information does not satisfy the AA similarity.

✨ Expert's Tip ✨

Other ways of determining similarity are SAS (Side, Angle, Side) and SSS (Side, Side, Side). The ratios of sides must be the same, the sides do not have to be identically sized.