SAT Math Multiple Choice Practice Question 38: Answer and Explanation
In this diagram (not drawn to scale), , and AG = GF. The length of AB is
Correct Answer: E
E. Because this problem involves parallel lines, you need to look for angles that are congruent. You can find them by looking for lines that make a Z or a backwards Z. Looking first at the bigger triangles, you can mark the diagram as follows:
Notice that the two angles in the middle are vertical, so they're also equal. This diagram is a?picture of similar triangles: Segment AC matches segment CD, segment CF matches segment CE, and segment AF matches segment DE. Therefore, you can use a ratio to figure out
the length of AC: .
Cross-multiplying your ratio tells you that 18(AC) = 288, and AC = 16. Now, because , triangle ABG is similar to ACF, as well. And because AG = GF, the line GB cuts triangle ACF in half, which means that AB is half the length of AC, or 8.
Be very careful that you match up the right parts when you write a ratio. Otherwise, you'll undoubtedly get the wrong answer. For example, if you ma