Young Geniuses · Ages 13 to 14
Circle Theorems Fill-in
Find missing angles using circle theorems. A Grade 8–9 geometry worksheet with five levels and answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Circle Theorems Fill-in
Circle Theorems Fill-in develops upper-secondary geometry reasoning by asking learners to find missing angles using the circle theorems. Each question describes a configuration and the relevant theorem — the angle at the centre being twice the angle at the circumference, the angle in a semicircle being a right angle, opposite angles of a cyclic quadrilateral summing to one hundred and eighty degrees, or angles in the same segment being equal — and the student applies it to find the unknown angle. The circle theorems are a cornerstone of Grade 8 to 9 geometry across the UK, and feature in the geometry strands of the US, Canadian and Australian curricula. They reward careful reasoning and a precise grasp of how angles around and within a circle are related. Working through varied configurations builds both recall of the theorems and the judgement to choose the right one. Because the given angles change each time, the worksheet stays fresh and reusable, and the five levels mix the theorems so students must identify which applies. Each page prints cleanly on a standard A4 sheet, and every level downloads with its own answer key giving each missing angle. There is no advertising and no sign-up.
Common questions
- Which theorems are covered?
- Angle at the centre, angle in a semicircle, cyclic quadrilaterals and angles in the same segment.
- What grade is this for?
- Grade 8 to Grade 9 learners aged 13 to 14.
- Is an answer key included?
- Yes, every level gives each missing angle.
A hand for grown-ups
- Before you start
- Point out a few shapes in the room first. Geometry starts with noticing, and it is everywhere.
- While they work
- Encourage them to turn shapes around and look from different angles — literally, with a real object if there is one.
- Afterwards
- Go on a shape hunt around the house together. Naming real shapes cements the vocabulary.
- Watch out for
- Thinking a rotated square is a "diamond", or that size changes what a shape is. Turning a real cut-out shows it is the same shape.
- Away from the screen
- Spot shapes on a walk, build with blocks, fold paper into shapes. Talk about corners and sides.
Where to go next
Chosen by the skills this activity practises.