Geometry and TrigonometryMediumCorresponding sides of similar triangles
Geometry and Trigonometry practice question
Triangle ABC is similar to triangle DEF, with vertices A, B, C corresponding to D, E, F respectively. AB = 6, DE = 9, and BC = 8. What is the length of EF?
- A. 12Correct
- B. 11
- C. 16/3
- D. 13.5
Answer: A. 12
Corresponding sides of similar triangles are in the same ratio. DE/AB = 9/6 = 3/2, so every side of DEF is 3/2 times the matching side of ABC. EF = (3/2)(8) = 12.
Why the other answers are wrong
- B. 11
- You added 3 to 8 because DE is 3 more than AB. Similar triangles are related by a MULTIPLYING factor (3/2 here), not by adding a fixed amount.
- C. 16/3
- 16/3 is 8 × (6/9) — the ratio is upside down. DEF is the LARGER triangle, so EF is larger than BC, not smaller.
- D. 13.5
- 13.5 is 9 × (9/6): the scale factor was applied to DE instead of to BC. EF corresponds to BC, so scale BC.
More Geometry and Trigonometry questions
- Medium
In a 45°-45°-90° right triangle, each leg has length 5. What is the length of the hypotenuse? - Medium
A cylinder has a radius of 3 and a height of 10. What is its volume? (Use V = πr²h.) - Medium
In a right triangle, the side opposite angle θ has length 3 and the hypotenuse has length 5. What is sin θ? - Medium
Two triangles are similar with a ratio of 2 to 3. A side of the smaller triangle measures 8. What is the lengt… - Medium
What is the distance between the points (1, 2) and (4, 6) in the coordinate plane? - Medium
A circle has a radius of 6. What is the area of a sector with a central angle of 60°?
Not affiliated with the College Board. SAT is a trademark of the College Board.