Enhance Your Skills with Our ACT Geometry Practice Test/Quiz

Report a question

What's wrong with this question?
You cannot submit an empty report. Please add some details.

30 random questions |30 minutes | Questions are randomized every attempt. Good luck!

ACT Math - Geometry Practice Test

Test your ACT geometry skills with 30 random practice test questions covering shapes, angles, and measurements!

1 / 27

1. If the radius of a circle doubles, by what factor does its area increase?

A) π

B) 2

C) 8

D) 4

New area = π(2r)² = 4πr². Area increases by factor of 4.

2 / 27

2. What is the surface area of a hemisphere with radius 4?

A) 32π

B) 24π

C) 48π

D) 16π

Curved SA=2πr²=32π. Base=πr²=16π. Total=48π.

3 / 27

3. In a 45-45-90 triangle, if the hypotenuse is 6, what is a leg?

A) 6√2

B) 3√2

C) 3

D) √6

Leg=6/√2=3√2.

4 / 27

4. What is the distance from point (3,4) to the line y=0?

A) 4

B) 0

C) 3

D) 5

Distance from (3,4) to y=0 is the y-coordinate=4.

5 / 27

5. A right triangle has legs 3 and 4. What is the hypotenuse?

A) 25

B) 5

C) 6

D) 7

Explanation: c² = 3² + 4² = 9 + 16 = 25, so c = 5

6 / 27

6. A regular polygon has exterior angle 45°. How many sides?

A) 7

B) 9

C) 6

D) 8

n=360/45=8 sides.

7 / 27

7. What is the y-coordinate of the midpoint of (3,7) and (9,1)?

A) 6

B) 8

C) 4

D) 5

y-midpoint = (7+1)/2 = 4.

8 / 27

8. A circle has arc length 8π with a 60° central angle. What is the radius?

A) 30

B) 12

C) 24

D) 20

8π=(60/360)(2πr)=πr/3. r=24.

9 / 27

9. What is the measure of the angle formed by a tangent and a chord at the point of tangency if the arc is 110°?

A) 55°

B) 70°

C) 110°

D) 220°

Tangent-chord angle=½ arc=55°.

10 / 27

10. What is the volume of a cube with side 4?

A) 16

B) 64

C) 24

D) 48

Explanation: Volume = s³ = 4³ = 64

11 / 27

11. What is the area of an annulus with outer radius 8 and inner radius 5?

A) 64π

B) 39π

C) 25π

D) 89π

A=π(64-25)=39π.

12 / 27

12. What is the area of a parallelogram with base 8 and height 5?

A) 20

B) 30

C) 40

D) 45

A = base × height = 8 × 5 = 40.

13 / 27

13. What is the measure of each interior angle of a regular hexagon?

A) 135°

B) 150°

C) 120°

D) 108°

(6-2)×180°/6 = 720°/6 = 120°.

14 / 27

14. A rectangle has perimeter 30 and length 10. What is its width?

A) 6

B) 4

C) 7

D) 5

2(10+w) = 30 → 10+w = 15 → w = 5.

15 / 27

15. What is the diagonal of a rectangular prism 3×4×5?

A) √52

B) √50

C) √53

D) √54

d=√(9+16+25)=√50=5√2.

16 / 27

16. Two chords in a circle intersect inside. One chord is divided into segments 3 and 4, the other into segments 2 and x. What is x?

A) 6

B) 4

C) 5

D) 8

Intersecting chords: 3×4 = 2×x → 12 = 2x → x = 6.

17 / 27

17. A right triangle has one leg 8 and hypotenuse 17. What is the other leg?

A) 13

B) 9

C) 15

D) 11

b = √(17²-8²) = √(289-64) = √225 = 15.

18 / 27

18. A circle has diameter 14. What is its circumference?

A) 14π

B) 28π

C) 49π

D) 7π

Explanation: Circumference = πd = 14π

19 / 27

19. If the perimeter of a square equals the circumference of a circle, and the square has side 5, what is the circle's radius?

A) 5π

B) 5/π

C) 20/π

D) 10/π

Square P=20. Circle C=20. 2πr=20. r=10/π.

20 / 27

20. If two lines have slopes 2 and -1/2, they are:

A) Equal

B) Perpendicular

C) Parallel

D) Neither

m₁×m₂=2×(-1/2)=-1. Perpendicular.

21 / 27

21. What is the locus of points equidistant from two parallel lines?

A) A circle between them

B) An ellipse

C) A line parallel to both halfway between them

D) A perpendicular bisector

The locus is the line halfway between, parallel to both.

22 / 27

22. What is the equation of a circle centered at (2,-3) with radius 5?

A) (x-2)²+(y+3)²=25

B) (x-2)²+(y+3)²=5

C) (x-2)²+(y-3)²=25

D) (x+2)²+(y-3)²=25

(x-h)²+(y-k)²=r². (x-2)²+(y-(-3))²=25.

23 / 27

23. A circle has area 64π. What is its circumference?

A) 32π

B) 16π

C) 8π

D) 64π

r²=64→r=8. C=2π(8)=16π.

24 / 27

24. What is the area of a triangle with base 10 and height 6?

A) 60

B) 120

C) 16

D) 30

Explanation: Area = ½ × base × height = ½ × 10 × 6 = 30

25 / 27

25. What is the distance from the origin to the point (5, 12)?

A) 17

B) 7

C) 15

D) 13

d = √(5²+12²) = √(25+144) = √169 = 13.

26 / 27

26. What is the sum of interior angles of a quadrilateral?

A) 360°

B) 270°

C) 540°

D) 450°

(4-2)×180=360°.

27 / 27

27. Two parallel lines are cut by a transversal. Alternate interior angles are:

A) Adjacent

B) Complementary

C) Equal

D) Supplementary

Explanation: Alternate interior angles are always equal

Your score is
The average score is 48%
0%

🎯 Register FREE to save your score and unlock 1000+ more free quizzes!

👉 Register Now — It’s Free!

📚 StudyRightWay

Pages

Resources

Legal

Connect

Course has been added to your cart