8th grade geometry
8th grade geometry (class 8): a picture quiz for kids, then every skill in order with lessons, a checklist and a plan.
🧒 Kids: answer 10 grade 8 geometry questions. Look at each picture and tap Check ✓!
What 8th grader learn in geometry
In grade 8, children move shapes with translations, reflections, rotations and dilations, use angle facts for parallel lines and triangles, prove and use the Pythagorean theorem, and find the volume of cylinders, cones and spheres.
- 8.G.A.1–4: properties of rotations, reflections and translations; congruence and similarity through transformations; coordinates after a move.
- 8.G.A.5: angle sums and exterior angles of triangles, angles made by parallel lines and a transversal.
- 8.G.B.6–8: explain a proof of the Pythagorean theorem and its converse, use it in 2D and 3D, and find distances between points.
- 8.G.C.9: the volume formulas for cones, cylinders and spheres.
The big idea in grade 8
Grade 8 geometry is about moving shapes and proving facts. Translations, reflections and rotations keep size and shape; dilations change size (8.G.A.1–4).
Children use angle facts for parallel lines and triangles (8.G.A.5), explain and use the Pythagorean theorem (8.G.B.6–8), and find the volume of cylinders, cones and spheres (8.G.C.9).
It is the bridge to high school geometry. The habit to build is giving a reason for every step: “equal because they are corresponding angles”.
When your child gets stuck
Most grade 8 trouble with the Pythagorean theorem is adding when finding a short side. If the hypotenuse is known, subtract.
For transformations, trace the shape on tracing paper and actually slide, flip or turn it. For volumes, check the radius: many wrong answers use the diameter.
8th grade geometry skills, in order
Work down the list. Each lesson explains the idea for parents with pictures and has a quiz for your child.
By the end of grade 8, your child should be able to…
- Name a move as a translation, reflection, rotation or dilation.
- Give the new coordinates after a reflection in an axis.
- Find a missing angle using parallel lines and a transversal.
- Find the hypotenuse of a right triangle, and a missing leg.
- Say whether 9, 12, 15 is a right triangle.
- Find the volume of a cylinder and a cone with the same radius and height.
Unsure where your child is? The geometry levels page has a short test for every step from naming shapes to the Pythagorean theorem.
A 4-week plan for 8th grade geometry
| When | Focus |
|---|---|
| Week 1 | Transformations on a grid, congruence and similarity |
| Week 2 | Angle relationships and angles in a triangle |
| Week 3 | The Pythagorean theorem and distance |
| Week 4 | Volume of cylinders, cones and spheres |
Add 5 minutes a day with the geometry practice tool, and check any area or perimeter answer with the area and perimeter calculator.
More for grade 8
All 8th grade math · CBSE class 8: The Baudhayana–Pythagoras Theorem · 8th grade exponents · Geometry quiz for grades 2 to 8 · Geometry for kids
What to say to your child
A short script for teaching it the first time. Pause after each line and let your child do the next step.
- “Is the new shape the same size? Facing the same way?”
- “What do the angles in a triangle add up to?” (180°.)
- “Which side is the hypotenuse?”
- “Add or subtract?”
- “What is the radius if the diameter is 10?” (5.)
More worked examples
Example 1: reflection
Reflect (3, 2) in the y-axis: (−3, 2).
Example 2: Pythagoras
Legs 6 and 8: √(36 + 64) = 10.
Example 3: volume
Cylinder r = 3, h = 5: 3.14 × 9 × 5 = 141.3; the cone is a third: 47.1.
Practice questions (answers below)
Ask these out loud or write them down. Check each answer, and ask “how did you get that?” for one or two.
- Reflect (4, 1) in the x-axis
- Rotate (2, 0) 180° about the origin
- Angles 50° and 60° in a triangle. Third?
- Co-interior angle to 75°
- Legs 5 and 12: hypotenuse
- Hypotenuse 10, leg 6: other leg
- Is 7, 24, 25 right?
- Cylinder r = 2, h = 10 (π ≈ 3.14)
- Sphere r = 3 (π ≈ 3.14)
- Stretch: distance (1, 1) to (4, 5)
Show the answers
- (4, −1)
- (−2, 0)
- 70°
- 105°
- 13
- 8
- yes
- 125.6
- 113.04
- 5
Common mistakes
How to teach it at home
Five minutes a day
Short daily practice beats long weekend sessions.
Draw it
Keep squared paper handy: most geometry is easier once it is drawn.
Shape spotting
Look for angles, parallel lines, symmetry and 3D shapes on walks and in the kitchen.
By grade
- Before: circles, angle relationships and surface area in grade 7: circumference and area of a circle
- After: high school geometry: proofs, similarity and trigonometry
Not sure where to start?
The free 8th grade math check-up tests every grade 8 topic in 15–20 minutes. It shows which topics are solid and which lesson to start with.
Worksheets and practice
Pythagorean theorem worksheet: printable PDF with an answer key. · Make a fresh test
Last reviewed
Questions parents ask
What geometry do 8th graders learn?
Transformations, congruence and similarity, angle facts for parallel lines and triangles, the Pythagorean theorem and distance, and the volume of cylinders, cones and spheres.
Is the Pythagorean theorem taught in 8th grade?
Yes. Common Core 8.G.B.6–8 covers the proof, its converse, finding missing sides and finding distances on a grid.
Is there a 8th grade geometry quiz?
Yes. The quiz at the top of this page has 10 mixed grade 8 questions, each with a picture. Every answer is marked straight away, and a wrong answer shows the working. Play again for a fresh set, or try the geometry quiz for grades 2 to 8.
What geometry is taught in class 8 in India?
The NCERT books spread geometry across every class: shapes and patterns early on, then perimeter, area, angles and symmetry, and later circles, constructions and the Pythagoras theorem. This page lists the skills in order, starting with transformations, angle relationships.
How much geometry practice does a 8th grader need?
About 10 minutes a day during a geometry unit: 5 minutes on the current skill with the practice tool and 5 minutes of mixed review. Drawing on squared paper counts too.