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Question 1
GeometryFoundation

Geometry practice question 1

Geometry practice topics

Question sets mix direct skills with unfamiliar applications so method selection becomes part of the practice.

01

Congruence, similarity, and proof

Use a scale factor to find missing sides, match corresponding parts, and justify each step with a stated rule.

02

Right triangles and circles

Apply the Pythagorean theorem and trigonometric ratios, and calculate arc lengths, sector areas, and circle measures.

03

Coordinate geometry

Find distances, midpoints, slopes, and missing endpoints from coordinates instead of from a drawn diagram.

04

Area, surface area, and volume

Calculate areas and volumes for prisms, cylinders, cones, and spheres, and work backwards from a volume to a length.

Geometry practice questions with worked answers

These 8 questions are printed in full on this page, with every step of the arithmetic written out. Cover the options, solve the question on paper first, and only then open the worked answer to compare your method with the one shown.

Question 1: Two triangles are similar. A side of 6 cm on the small triangle matches a side of 15 cm on the large one. Another small-triangle side is 8 cm. How long is the matching large-triangle side?

Foundation level · congruence, similarity, and proof

  1. 20 cm
  2. 17 cm
  3. 18 cm
  4. 24 cm
Show the worked answer
  1. Similar triangles have one scale factor for every pair of matching sides.
  2. The scale factor is 15 / 6 = 2.5.
  3. Multiply the 8 cm side by the same factor: 8 x 2.5.
  4. 8 x 2.5 = 20, so the matching side is 20 cm.

Answer: 20 cm

Question 2: In triangle ABC, angle A = 47 degrees and angle B = 68 degrees. Triangle ABC is congruent to triangle DEF. What is angle F?

Exam level · congruence, similarity, and proof

  1. 65 degrees
  2. 47 degrees
  3. 68 degrees
  4. 115 degrees
Show the worked answer
  1. The three angles of any triangle add to 180 degrees.
  2. Angle C = 180 - 47 - 68.
  3. 180 - 47 = 133, and 133 - 68 = 65, so angle C = 65 degrees.
  4. Congruent triangles have equal matching angles, and F matches C, so angle F = 65 degrees.

Answer: 65 degrees

Question 3: A right triangle has legs of 9 cm and 12 cm. How long is the hypotenuse?

Foundation level · right triangles and circles

  1. 15 cm
  2. 21 cm
  3. 13 cm
  4. 18 cm
Show the worked answer
  1. Use a^2 + b^2 = c^2 with a = 9 and b = 12.
  2. 9^2 = 81 and 12^2 = 144.
  3. 81 + 144 = 225, so c^2 = 225.
  4. The square root of 225 is 15, so the hypotenuse is 15 cm.

Answer: 15 cm

Question 4: A circle has a radius of 8 cm. What is the area of a 90 degree sector? Use pi = 3.14.

Exam level · right triangles and circles

  1. 50.24 cm^2
  2. 200.96 cm^2
  3. 12.56 cm^2
  4. 25.12 cm^2
Show the worked answer
  1. The whole circle has area pi x r^2 = 3.14 x 8^2.
  2. 8^2 = 64, so the full area is 3.14 x 64 = 200.96 cm^2.
  3. A 90 degree sector is 90/360 = one quarter of the circle.
  4. 200.96 / 4 = 50.24, so the sector area is 50.24 cm^2.

Answer: 50.24 cm^2

Question 5: What is the distance between the points (-3, 2) and (5, 8)?

Exam level · coordinate geometry

  1. 10
  2. 14
  3. 8
  4. square root of 28
Show the worked answer
  1. Find the horizontal gap: 5 - (-3) = 8.
  2. Find the vertical gap: 8 - 2 = 6.
  3. The distance is the hypotenuse of an 8 by 6 right triangle: 8^2 + 6^2 = 64 + 36 = 100.
  4. The square root of 100 is 10, so the distance is 10.

Answer: 10

Question 6: A line segment has one endpoint at (-4, 7) and its midpoint at (1, 3). What are the coordinates of the other endpoint?

Challenge level · coordinate geometry

  1. (6, -1)
  2. (-9, 11)
  3. (5, -4)
  4. (2, 5)
Show the worked answer
  1. The midpoint is the average of the two endpoints, so (-4 + x)/2 = 1.
  2. Multiply by 2: -4 + x = 2, so x = 6.
  3. Do the same for y: (7 + y)/2 = 3, so 7 + y = 6 and y = -1.
  4. The other endpoint is (6, -1). Check: the midpoint of (-4, 7) and (6, -1) is (1, 3).

Answer: (6, -1)

Question 7: A cylinder has a radius of 5 cm and a height of 10 cm. What is its volume? Use pi = 3.14.

Foundation level · area, surface area, and volume

  1. 785 cm^3
  2. 157 cm^3
  3. 1570 cm^3
  4. 314 cm^3
Show the worked answer
  1. Volume of a cylinder = area of the circular base x height.
  2. Base area = 3.14 x 5^2 = 3.14 x 25 = 78.5 cm^2.
  3. Multiply by the height: 78.5 x 10.
  4. 78.5 x 10 = 785, so the volume is 785 cm^3.

Answer: 785 cm^3

Question 8: A cube has a volume of 216 cm^3. What is its total surface area?

Challenge level · area, surface area, and volume

  1. 216 cm^2
  2. 144 cm^2
  3. 36 cm^2
  4. 1296 cm^2
Show the worked answer
  1. Volume of a cube is side x side x side, so the side is the cube root of 216.
  2. 6 x 6 x 6 = 216, so each side is 6 cm.
  3. One face has area 6 x 6 = 36 cm^2, and a cube has 6 faces.
  4. 6 x 36 = 216, so the surface area is 216 cm^2 (the same number as the volume, but different units).

Answer: 216 cm^2

How the three Geometry difficulty levels differ

The difficulty buttons above change what a question asks of you, not just the size of the numbers. Each example below is taken from the question set on this page.

Difficulty levels for Geometry practice, with an example question from this page.
LevelWhat it testsExample questionTime target
FoundationOne skill at a time, with the numbers kept small enough to check in your head.Two triangles are similar. A side of 6 cm on the small triangle matches a side of 15 cm on the large one. Another small-triangle side is 8 cm. How long is the matching large-triangle side?About 1 minute
ExamThe wording of a real test paper: pick the method first, then carry out two or three steps.In triangle ABC, angle A = 47 degrees and angle B = 68 degrees. Triangle ABC is congruent to triangle DEF. What is angle F?2 to 3 minutes
ChallengeTwo ideas combined, or a result you have to interpret after the calculation ends.A line segment has one endpoint at (-4, 7) and its midpoint at (1, 3). What are the coordinates of the other endpoint?4 to 5 minutes

How to practice Geometry effectively

Begin without notes and explain your choice before checking. For every miss, identify whether the cause was a definition, setup, calculation, interpretation, or time decision. Re-solve the question from a blank page, then return to the same skill in a mixed set tomorrow.

What your Geometry answer review should show

A useful review shows more than the correct option. Compare the method with your first attempt, locate the earliest incorrect decision, and write one rule that would prevent the same error in a new Geometry problem.

Move from mixed Geometry questions to a complete course

This page targets flexible Geometry question practice. When you need a syllabus-aligned sequence with unit selection, use Geometry practice by unit and return here later for mixed retrieval.

Questions about Geometry practice

When should I change the difficulty?

Move up after you can solve several questions accurately without hints and explain the method. Move down for one short set when errors show that a definition or setup is still uncertain.

How often should I practice?

Short sessions on several days usually build stronger recall than one long session. Revisit missed Geometry skills the next day, then mix them with older topics later in the week.

Where can I review the lessons in order?

Use Geometry practice by unit for a syllabus-aligned sequence with unit selection, practice, and a complete answer review.

Stuck on a problem?

Stuck on a Geometry question?

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