Bluebook SAT Test Lines, Angles, and Triangles 4 — Questions and Answers
Question 1: Two similar triangles have corresponding sides in ratio 3:7. A side of the smaller triangle is 12 cm. What is the corresponding side of the larger?
- 21 cm
- 24 cm
- 28 cm (Correct answer)
- 36 cm
Correct answer: 28 cm
3/7 = 12/x → x = 84/3 = 28 cm.
Question 2: Three angles on a straight line are x, 2x, and 3x. What is x?
- 15°
- 20°
- 30° (Correct answer)
- 45°
Correct answer: 30°
x + 2x + 3x = 180° → 6x = 180° → x = 30°.
Question 3: A transversal crosses two parallel lines. Corresponding angles are (7x − 4)° and (5x + 20)°. What is x?
- 8
- 10
- 12 (Correct answer)
- 14
Correct answer: 12
7x − 4 = 5x + 20 → 2x = 24 → x = 12.
Question 4: In triangle DEF, angle D = 2 × angle E, and angle F = 60°. What is angle D?
- 40°
- 60°
- 80° (Correct answer)
- 120°
Correct answer: 80°
D = 2E; 2E + E + 60 = 180 → E = 40°; D = 80°.
Question 5: Which set of side lengths CANNOT form a triangle?
- 3, 4, 5
- 6, 8, 10
- 5, 12, 13
- 2, 3, 7 (Correct answer)
Correct answer: 2, 3, 7
Triangle inequality: 2 + 3 = 5 < 7, violating the rule that any two sides must sum to more than the third.
Question 6: Two adjacent angles at an intersection are (8x + 5)° and (4x + 55)°. If they are supplementary, what is x?
- 5
- 10 (Correct answer)
- 15
- 20
Correct answer: 10
(8x+5)+(4x+55)=180 → 12x+60=180 → x=10.
Question 7: Triangles ABD and ACE share angle A, with AB = 6, AD = 4, and AC = 9. If the triangles are similar, what is AE?
- 4
- 6 (Correct answer)
- 6.67
- 12
Correct answer: 6
AB/AC = AD/AE → 6/9 = 4/AE → AE = 6.
Bluebook SAT Test Lines, Angles, and Triangles 4
Two similar triangles have corresponding sides in ratio 3:7.
A side of the smaller triangle is 12 cm.
What is the corresponding side of the larger?