NJSLA Geometric Principles and Measurement 2 — Questions and Answers
Question 1: A triangle has angles measuring 47° and 63°. What is the measure of the third angle?
- 60°
- 70° (Correct answer)
- 80°
- 90°
Correct answer: 70°
The sum of angles in a triangle is 180°, so 180 − 47 − 63 = 70°.
Question 2: A rectangle has a length of 12 cm and a width of 5 cm. What is the length of its diagonal?
- 11 cm
- 13 cm (Correct answer)
- 15 cm
- 17 cm
Correct answer: 13 cm
Using the Pythagorean theorem: √(12² + 5²) = √(144 + 25) = √169 = 13 cm.
Question 3: Which transformation maps a figure to a congruent figure in a different position without changing its size or shape?
- Dilation
- Reflection
- Rotation
- Both B and C (Correct answer)
Correct answer: Both B and C
Both reflections and rotations are rigid motions that produce congruent figures with no size change.
Question 4: A cylinder has a radius of 4 inches and a height of 10 inches. What is its volume? (Use π ≈ 3.14)
- 160.8 in³
- 502.4 in³ (Correct answer)
- 251.2 in³
- 200.96 in³
Correct answer: 502.4 in³
Volume = π r² h = 3.14 × 16 × 10 = 502.4 in³.
Question 5: Two lines are cut by a transversal. If the co-interior (same-side interior) angles measure 112° and 68°, what is true about the two lines?
- They are perpendicular
- They are parallel (Correct answer)
- They intersect at 44°
- They are skew lines
Correct answer: They are parallel
Co-interior angles are supplementary (sum = 180°) when lines are parallel; 112 + 68 = 180, so the lines are parallel.
Question 6: A square has a perimeter of 36 meters. What is its area?
- 81 m² (Correct answer)
- 72 m²
- 64 m²
- 54 m²
Correct answer: 81 m²
Each side = 36 ÷ 4 = 9 m, so area = 9² = 81 m².
Question 7: A cone has a radius of 3 cm and a height of 8 cm. Which expression correctly represents its volume?
- π(3)²(8)
- (1/3)π(3)²(8) (Correct answer)
- (1/2)π(3)²(8)
- π(3)(8)
Correct answer: (1/3)π(3)²(8)
Volume of a cone = (1/3)πr²h = (1/3)π(9)(8).
NJSLA Geometric Principles and Measurement 2
A triangle has angles measuring 47° and 63°.
What is the measure of the third angle?