7th Math: Geometry practice questions and exam guide

The circumference of a circle with radius 7 is approximately (π ≈ 3.14):

1. 21.98
2. 49
3. 43.96
4. 153.86

Answer: C — 43.96

C) C = 2πr ≈ 2(3.14)(7) ≈ 43.96. A) Used πr only. B) r². D) Area, not circumference.

A composite figure consists of a 6×4 rectangle with a semicircle (diameter 4) attached. Area (π ≈ 3.14):

1. 24
2. 36.56
3. 30.28
4. 48.56

Answer: C — 30.28

C) Rect = 24; semicircle = ½·π·2² = 6.28; total ≈ 30.28. A) Forgot semicircle. B) Used full circle (12.56). D) Doubled.

Supplementary angles sum to:

1. 90°
2. 180°
3. 360°
4. 270°

Answer: B — 180°

B) Standard. A/C/D) Different.

What cross-section is formed when a cylinder is cut perpendicular to its height?

1. Square
2. Rectangle
3. Circle
4. Ellipse

Answer: C — Circle

A horizontal cut perpendicular to the axis gives a circle. (A/B) not round; (D) an angled cut gives an ellipse, not perpendicular.

Area of circle with radius 5 (π ≈ 3.14):

1. 15.7
2. 31.4
3. 78.5
4. 25

Answer: C — 78.5

C) A = πr² = 3.14·25. A/B/D) Each is incorrect.

Triangle sum:

1. 180°
2. 360°
3. 90°
4. Varies

Answer: A — 180°

A) Standard. B/C/D) Each is incorrect.

Which figure has exactly one pair of parallel sides?

1. Parallelogram
2. Rectangle
3. Trapezoid
4. Rhombus

Answer: C — Trapezoid

A trapezoid has exactly one pair of parallel sides. Parallelogram, rectangle, and rhombus all have two pairs of parallel sides.

Area of a triangle with base 9 and height 6:

1. 54
2. 27
3. 15
4. 36

Answer: B — 27

B) ½·9·6 = 27. A) Forgot ½. C) Added 9+6. D) Used 6·6.

A cylinder has radius 4 and height 10. Volume (π ≈ 3.14):

1. 502.4
2. 251.2
3. 125.6
4. 1004.8

Answer: A — 502.4

A) V = πr²h = 3.14·16·10 = 502.4. B) Used r not r². C) Used (1/2)πr²h. D) Doubled.

A scale model car is 6 inches long; the real car is 12 feet long. Scale ratio (model:real)?

1. 1:2
2. 1:6
3. 1:12
4. 1:24

Answer: D — 1:24

Convert: 12 feet = 144 inches; ratio = 6:144 = 1:24. (A) ignored units; (C) used feet directly; (B) only divided by 6.

Two angles are complementary. One is 24°. The other is:

1. 156°
2. 76°
3. 66°
4. 336°

Answer: C — 66°

C) 90 − 24 = 66°. A) Used supplement. B) Arithmetic. D) Subtracted from 360°.

Two angles form a linear pair. One is 3x + 10 and the other is x + 50. Find x.

1. 20
2. 30
3. 15
4. 25

Answer: B — 30

Linear pair sums to 180°: (3x + 10) + (x + 50) = 180 → 4x + 60 = 180 → 4x = 120 → x = 30. (A) solved 4x = 80; (C/D) arithmetic errors.

Can you make a triangle with sides 5, 7, and 9?

Yes. 5+7 = 12 > 9; 5+9 > 7; 7+9 > 5.

What are 'complementary angles'?

Two angles that add up to 90°.

Two angles are supplementary, one is 3x and the other is 60. Find x.

x = 40. (3x + 60 = 180; 3x = 120; x = 40.)

What are 'adjacent angles'?

Two angles that share a vertex and a side but no overlap.

WORKED EXAMPLE — Two lines intersect; one angle is 105°. Find the vertical angle.

STEP 1 — Vertical angles are formed by two intersecting lines opposite each other. STEP 2 — Vertical Angles Theorem: vertical angles are congruent (equal). STEP 3 — The angle opposite the 105° angle is therefore also 105°. STEP 4 — Sanity check: the two linear-pair angles would each be 75° (since 180 − 105 = 75) and they too match each other. ANSWER: 105°.

WORKED EXAMPLE — Two angles are complementary and form a right angle. One is 38°. Find the other.

STEP 1 — Complementary angles sum to 90°. STEP 2 — Write: 38 + x = 90. STEP 3 — Subtract: x = 90 − 38. STEP 4 — Compute: x = 52°. STEP 5 — Check: 38 + 52 = 90 ✓. ANSWER: 52°.