# SAT Math Multiple Choice Question 969: Answer and Explanation

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**Question: 969**

**5.**

In the figure above,andare parallel andintersectsat *V*. What is the length of?

- A. 8
- B. 9
- C. 10
- D. 12

**Correct Answer:** A

**Explanation:**

**A**

**Difficulty:** Hard

**Category:** Additional Topics in Math / Geometry

**Strategic Advice:** When comparing similar (or congruent) triangles that are oriented differently, be sure to mark any corresponding sides and angles with hash marks so that you keep them in the correct order.

**Getting to the Answer:** Start by filling in as much information as you can on the diagram. ∠*WVX* is congruent to ∠*YVU* because they are vertical angles, so mark these angles with a single hash mark. Also note that because *UY* is parallel to *WX*, ∠*W* is congruent to ∠*Y*, and ∠*X* is congruent to ∠*U* (both pairs are alternate interior angles). Mark these pairs with double and triple hash marks. Your diagram might look like the following:

Use the hash marks to write a similarity statement-start with the angles marked with one hash mark, then two hash marks, then three: Δ*VWX* ~ Δ*VYU*. The order of the letters in the similarity statement makes it clear that *VX* (first and last letter) corresponds to *VU* (first and last letter) and is triple the length (based on the figure). Segment *VW* (first and second letter) is therefore one-third the length of *VY* (first and second letter), which is 6 ÷ 3 = 2. The question asks for the length of *WY*, which is 2 + 6 = 8. (A) is the correct answer.