Circle Theorem: Angle in a Semicircle — Interactive Lesson (Ages 14–16)

Where is the right angle in a semicircle? This 25-slide interactive lesson teaches the theorem on angles in a semicircle, with clear reasons for each step.

Mastering Angles in a Semicircle at GCSE

Students learn the second circle theorem: when a triangle is drawn in a semicircle, the angle formed on the circumference is 90°. A worked example finds several angles in one diagram, using reasons such as angles at the base of an isosceles triangle, angles in a semicircle, angles in a triangle and angles on a line. Students then find angles in circles with a diameter and centre, including cases where both triangles are in a semicircle.

What’s Included

• 25-slide interactive lesson on the angle in a semicircle theorem
• A clear statement of the theorem
• A worked example with reasons for each angle
• Practice questions on circles with a diameter and centre
• Fill-in-the-blank questions and a review quiz with instant feedback

Key Benefits for Students

• Builds understanding of why the angle is 90°
• Models how to give reasons for each step
• Combines circle theorems with isosceles and triangle facts
• Instant feedback on answer questions

Why Teachers Love It

• No prep — ready for whole-class teaching on an interactive whiteboard
• Worked examples model exam-style reasoning
• Self-marking questions support independent practice
• Suits teaching, revision and homework
• Fits neatly into a circle theorems unit

Love this? You’ll love…

• Circle Theorem: Cyclic Quadrilaterals — Interactive Lesson (Ages 14–16)
• Circle Theorem: Angles in the Same Segment — Interactive Lesson (Ages 14–16)
• Circle Theorems Tangents To A Circle — Interactive Lesson (KS4)

A dependable addition to a GCSE circle theorems unit, giving students a clear, reasoned approach to angle problems. Learning to justify each step is what earns the marks in the exam.

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FAQ

What year group is this for? Years 10–11 (ages 14–16), GCSE.

Does it show how to give reasons? Yes — the worked example gives a reason for every angle.

Is it self-marking? Yes, with instant feedback on the questions.