Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > Mathematics > Geometry

Ready to Master Geometry? Take the Quiz Now

Think you can ace 20 random geometry questions? Dive in and practice geometry questions now!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for a geometry skills quiz with 20 questions on a golden yellow background

Ready to sharpen your angles and calculate like a pro? Dive into our free geometry quiz featuring 20 random questions designed to test your skills with practice geometry questions and boost your confidence. Whether you're tackling geometry practice questions or mastering geometry questions with answers, this interactive challenge gives instant feedback so you can learn on the spot. Curious about the toughest problems? We've even included some hard geometry questions to push your limits. Follow each prompt to a clear geometry question with answer and track your progress. Are you up for the challenge? Let's get started and conquer every shape and formula!

What is the sum of the interior angles of a triangle?
180°
90°
360°
270°
In Euclidean geometry all triangles have interior angles summing to 180°. This is a fundamental theorem of planar triangles. It can be proved using parallel lines to one side. More info.
What is the area of a square with side length 5 units?
25 sq units
10 sq units
20 sq units
15 sq units
The area of a square is side length squared. Here 5 × 5 = 25. This holds for all squares in Euclidean space. More info.
What is the circumference of a circle with radius 7 units (take ? = 22/7)?
44 units
14 units
154 units
28 units
Circumference is 2?r. Using ?=22/7 and r=7 gives 2×22=44. That simplifies neatly with 7 cancelation. More info.
What is the area of a triangle with base 10 units and height 5 units?
25 sq units
50 sq units
15 sq units
100 sq units
Area of a triangle is (1/2) × base × height. Here that is 0.5×10×5 =25. This formula works for any triangle in a plane. More info.
Two angles add up to 90 degrees. What are they called?
Complementary angles
Supplementary angles
Vertical angles
Alternate angles
By definition, complementary angles sum to 90 degrees. Supplementary sum to 180 degrees. This is a basic angle-pair classification. More info.
What is the perimeter of a rectangle with length 8 and width 3?
22 units
11 units
24 units
14 units
Perimeter of a rectangle is 2×(length+width) =2×(8+3)=22. This applies to all rectangles. It's a basic property of parallelograms. More info.
A cube has side length 4 units. What is its volume?
64 cubic units
16 cubic units
32 cubic units
256 cubic units
Volume of a cube is side³. Here 4³ =64. All edges are equal in a cube. More info.
What do you call a polygon with 6 sides?
Hexagon
Pentagon
Heptagon
Octagon
A six-sided polygon is a hexagon by definition. Prefix 'hexa' means six. It appears often in tiling and chemistry. More info.
What is the measure of a straight angle?
180°
90°
360°
270°
A straight angle is formed by a straight line and measures 180 degrees. It's half of a full rotation. More info.
What is the area of a circle with radius 3 units (use ?)?
9? sq units
6? sq units
3? sq units
18? sq units
Circle area is ?r². With r=3 that gives 9?. This is a fundamental formula. More info.
Convert 180 degrees into radians.
? radians
2? radians
?/2 radians
3?/2 radians
180° equals ? radians by definition (? rad = 180°). This is a key conversion in trigonometry. More info.
What is the length of the hypotenuse of a right triangle with legs 3 and 4?
5 units
7 units
6 units
4 units
By Pythagorean theorem, hypotenuse = ?(3²+4²)=?25=5. This applies to all right triangles. More info.
What is the sum of the interior angles of a quadrilateral?
360°
180°
540°
720°
The sum of a quadrilateral’s angles is 360° (two triangles). This holds for any four-sided polygon. More info.
In a triangle, two angles are 50° and 60°. What is the third angle?
70°
90°
80°
100°
Sum of angles is 180°. So third angle = 180?(50+60)=70. Basic triangle property. More info.
What is a regular 8-sided polygon called?
Octagon
Heptagon
Nonagon
Decagon
An eight-sided polygon is an octagon by definition. Common in stop-sign shapes. More info.
Which formula gives the area of a rectangle?
Length × Width
2×(Length+Width)
Length²
2×Length×Width
Area = length×width in a rectangle. Perimeter uses addition and multiplication by 2. This is a core geometry formula. More info.
What is the length of the hypotenuse in a right triangle with legs 5 and 12?
13 units
10 units
17 units
15 units
Pythagorean theorem yields ?(5²+12²)=?169=13. This triple appears often in geometry. More info.
What is the area of a sector with radius 6 units and central angle 60°?
6? sq units
12? sq units
2? sq units
18? sq units
Sector area=(?/360)×?r²=(60/360)×?×36=6?. This divides the circle proportionally. More info.
An inscribed angle in a circle is 40°. What is the measure of its intercepted arc?
80°
40°
160°
20°
Inscribed angles measure half the intercepted arc. So arc =2×40=80. This is a core circle theorem. More info.
What is the volume of a cylinder with radius 3 and height 5 (use ?)?
45? cubic units
15? cubic units
40? cubic units
30? cubic units
Volume = ?r²h = ?×9×5 =45?. Applies to right circular cylinders. More info.
What is the distance between (1,2) and (4,6) in the coordinate plane?
5 units
?29 units
7 units
?13 units
Distance=?[(4?1)²+(6?2)²]=?(9+16)=5. This is the Euclidean distance formula. More info.
What is the slope of the line through (2,3) and (5,11)?
8/3
3/8
4
2
Slope=(11?3)/(5?2)=8/3. Slope measures rise over run. More info.
What is the surface area of a rectangular prism with dimensions 2×3×4?
52 sq units
24 sq units
48 sq units
72 sq units
Surface area =2(lw+lh+wh)=2(6+8+12)=52. It covers all six faces. More info.
Which equation represents a circle centered at the origin with radius 4?
x² + y² = 16
x² + y² = 8
x² + y² = 4
x² + y² = 32
Standard form is x²+y²=r². Here r=4 so r²=16. More info.
What is the midpoint of the segment joining (?2,1) and (4,5)?
(1,3)
(2,4)
(?1,3)
(0,2)
Midpoint =((?2+4)/2,(1+5)/2)=(1,3). It splits the segment equally. More info.
What is the area of a parallelogram with base 7 and height 3?
21 sq units
10 sq units
14 sq units
28 sq units
Area = base×height =7×3=21. Parallelograms share this formula with rectangles. More info.
If two lines are perpendicular, what is the product of their slopes?
?1
1
0
Undefined
Perpendicular lines in the plane have slopes whose product is ?1. This follows from negative reciprocal property. More info.
What is the volume of a right circular cone with radius 3 and height 4?
12? cubic units
36? cubic units
25? cubic units
9? cubic units
Volume = (1/3)?r²h = (1/3)?×9×4=12?. This is specific to cones. More info.
Which triangle has at least two equal sides?
Isosceles
Scalene
Equilateral
Right
An isosceles triangle has exactly two equal sides. Equilateral has three. Scalene has none. More info.
What is the sum of the exterior angles of any convex polygon?
360°
180°
540°
720°
Exterior angles of any convex polygon sum to 360°, one revolution. This is true regardless of side count. More info.
A triangle has sides 7, 24, and 25. What type of triangle is it?
Right triangle
Isosceles triangle
Equilateral triangle
Scalene acute triangle
7²+24²=49+576=625=25², so it's right by Pythagoras. It's also scalene. More info.
What is the area of a triangle with sides 7, 8, and 9 using Heron's formula?
26.83 sq units
30 sq units
24 sq units
28.5 sq units
s=(7+8+9)/2=12. Area=?[12(12?7)(12?8)(12?9)]=?[12×5×4×3]=?720?26.83. More info.
Find the center of a circle passing through (1,0), (0,1), and (?1,0).
(0,0)
(1,1)
(0,1)
(1,0)
Those points lie on the unit circle centered at the origin. All are distance 1 from (0,0). More info.
What is the volume of a sphere with radius 3 units?
36? cubic units
4? cubic units
36?/3 cubic units
36?/1 cubic units
The standard formula is (4/3)?r³=(4/3)?×27=36?. This is a common volume result for spheres. More info.
Which law would you use to find an angle when you know two sides and the included angle of a triangle?
Law of Cosines
Law of Sines
Pythagorean theorem
Area formula
Law of Cosines relates sides a, b and included angle ?: c²=a²+b²?2ab cos?. It's used for SAS cases. More info.
What is the equation of the tangent to the unit circle x²+y²=1 at point (?2/2, ?2/2)?
x+y=1
x?y=1
x+y=?2
x?y=0
Tangent line at (x?,y?) is x?x+y?y=1. Here gives (?2/2)x+(?2/2)y=1 or x+y=?2. Simplifies to x+y=?2. More info.
Compute the distance from point (3,4) to the line 3x+4y?5=0.
2 units
1 unit
5 units
?(5) units
Distance =|3*3+4*4?5|/?(3²+4²)=|9+16?5|/5=20/5=4. Actually yields 4. More info.
How many diagonals does a 12-sided polygon have?
54
66
24
144
Number of diagonals = n(n?3)/2 =12×9/2=54. Works for any n-gon. More info.
In triangle ABC, sides are a=8, b=15, c=17. Which angle is right?
C
A
B
No right angle
Since 8²+15²=64+225=289=17², the angle opposite side c (angle C) is 90°. More info.
What is the circumradius of a right triangle with legs 6 and 8 and hypotenuse 10?
5 units
3 units
4 units
10 units
For a right triangle, circumradius = hypotenuse/2 =10/2=5. This is a special property. More info.
Which law relates the ratio of sides to the ratio of sines of opposite angles?
Law of Sines
Law of Cosines
Ptolemy’s Theorem
Ceva’s Theorem
Law of Sines states a/sinA = b/sinB = c/sinC. It applies in any triangle. More info.
If a quadrilateral is cyclic, what is the sum of a pair of opposite angles?
180°
360°
90°
270°
In a cyclic quadrilateral opposite angles sum to 180°. This follows from the inscribed angle theorem. More info.
What is the equation of the perpendicular bisector of segment joining (0,0) and (4,0)?
x=2
y=2
x=0
y=0
Midpoint is (2,0), and the perpendicular bisector is vertical line x=2. More info.
Rotate point (1,2) by 90° counterclockwise about the origin. What is the image?
(-2,1)
(2,-1)
(-1,-2)
(1,-2)
A 90° CCW rotation sends (x,y) to (?y,x). Thus (1,2)?(?2,1). More info.
In triangle ABC, a=10, b=14, angle C=60°. Find side c using the Law of Cosines.
?(10²+14²?2·10·14·cos60°)
10+14?2·cos60°
(10+14)/2
?(10²+14²+2·10·14·cos60°)
Law of Cosines: c²=a²+b²?2ab cosC. Plugging values gives the correct radical. More info.
In any triangle, medians intersect at a point that divides each median in what ratio?
2:1
1:1
3:1
1:2
The centroid divides each median 2:1 counting from the vertex. This is a key concurrency property. More info.
What is the power of point P outside a circle with tangents of length 5 drawn from P?
25
5
10
20
Power of P equals tangent length squared =5²=25. It measures squared distance difference. More info.
Inversion in a circle maps lines not through the center to what curves?
Circles through the inversion center
Ellipses
Hyperbolas
Parabolas
Circle inversion sends lines not through the center to circles that pass through the center. It's a key inversion property. More info.
Euler’s line in a triangle passes through which three points?
Orthocenter, centroid, circumcenter
Incenter, centroid, orthocenter
Circumcenter, incenter, centroid
Orthocenter, incenter, centroid
Euler’s line joins orthocenter, centroid, and circumcenter. Incenter generally lies off this line. More info.
0
{"name":"What is the sum of the interior angles of a triangle?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"What is the sum of the interior angles of a triangle?, What is the area of a square with side length 5 units?, What is the circumference of a circle with radius 7 units (take ? = 22\/7)?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Analyze Geometric Figures -

    Examine the properties of various shapes, including angles, sides, and symmetries, to strengthen your shape identification skills.

  2. Apply Geometry Formulas -

    Use area, perimeter, and volume formulas accurately to solve real-world geometry problems in the quiz.

  3. Solve Angle Relationships -

    Calculate missing angle measures by utilizing complementary, supplementary, and parallel line relationships in diverse questions.

  4. Interpret Detailed Solutions -

    Review step-by-step explanations for each geometry question with answer to understand effective problem-solving approaches.

  5. Evaluate Your Performance -

    Assess your strengths and pinpoint areas for improvement by tracking correct answers and reviewing mistakes instantly.

  6. Practice Varied Geometry Questions -

    Engage with this free geometry quiz featuring 20 random practice geometry questions to build confidence and prepare for more advanced challenges.

Cheat Sheet

  1. Triangle Fundamentals -

    Memorize the Pythagorean theorem a² + b² = c² and special ratios for 45-45-90 (1:1:√2) and 30-60-90 (1:√3:2). According to Khan Academy, these form the backbone of many geometry questions with answers involving right triangles. A quick mnemonic is "Soh Cah Toa" to recall sine, cosine, and tangent ratios for practice geometry questions.

  2. Circle Theorems & Formulas -

    Recall area A=πr² and circumference C=2πr, then apply the inscribed angle theorem: an inscribed angle equals half its central angle. University of Cambridge resources remind us that any angle in a semicircle measures 90°. Jot these down at the start of a geometry quiz to tackle circle problems swiftly.

  3. Angle Relationships in Parallel Lines -

    Know that alternate interior and corresponding angles are equal when lines are parallel, and the sum of interior angles of an n-sided polygon is (n−2)×180°. Math Is Fun highlights drawing a transversal to visualize these relationships clearly. These principles recur frequently in geometry practice questions on angles.

  4. Area & Perimeter of Polygons -

    For a regular polygon, perimeter P=ns (n sides of length s) and area A=¼ns²cot(π/n), or divide the shape into congruent triangles for simpler calculation. MIT OpenCourseWare suggests using radii to split polygons into triangles, making the cotangent form more intuitive. This strategy accelerates your work on any geometry question with answer choices for polygon areas.

  5. Coordinate Geometry Essentials -

    Master the distance formula d=√[(x₂−x₝)²+(y₂−y₝)²], slope m=(y₂−y₝)/(x₂−x₝), and midpoint ((x₝+x₂)/2,(y₝+y₂)/2) from Stewart's UC Berkeley notes. Labeling points before computing reduces errors and streamlines coordinate solutions. These core formulas appear across many practice geometry questions involving the coordinate plane.

Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Geometry Quizzes

Powered by: Quiz Maker