Discovering Circle Theorems - Guided Inquiry & Reference Pack

Math Giraffe
Grade Levels
8th - 11th
Formats Included
  • PDF
9 plus answer keys & directions
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Math Giraffe


Circle Theorems & Properties - Discovery:

This lesson covers 10 circle theorems for high school Geometry. Students discover 4 theorems using guided half-sheet activities that require a protractor and straightedge.

Here's what's included:

- 4 half-page discoveries for the first four theorems

- Reference sheet with 10 theorems in color and in black & white (2 pages to be printed as a double-sided 8.5x11 poster)

- Recording sheets with 10 theorems for students to complete the theorem and draw a diagram (can be cut and assembled into a booklet)

The following theorems are included:

- Inscribed angles that intercept the same arc (or congruent arcs) are congruent.

- Radii of the same circle are congruent.

- A radius (or diameter) that is perpendicular to a chord bisects the chord.

- An angle inscribed in a semi-circle is a right angle.

- Arcs that intercept congruent chords are congruent.

- The segments from 2 tangent points to the point that the tangents meet outside the circle are congruent.

- A radius drawn to a tangent is perpendicular to the tangent.

- Chords that are congruent are equidistant from the center.

- The measure of an inscribed angle is half the measure of the central angle that intercepts the same arc.

- Opposite angles in an inscribed quadrilateral are supplementary.

** This resource is also available as part of a DISCOUNTED bundle: Circles Bundle

You may also like the following resources:

High School Geometry Super Bundle

Circles Proofs

Circle Theorems - Angle Puzzles

Total Pages
9 plus answer keys & directions
Answer Key
Teaching Duration
2 days
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to see state-specific standards (only available in the US).
Identify and describe relationships among inscribed angles, radii, and chords.
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Construct a tangent line from a point outside a given circle to the circle.


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