Circle Theorems Angles at the Circumference Demonstration This

Circle Theorems – Angles at the Circumference – Demonstration This resource provides animated demonstrations of the mathematical method. Check animations and delete slides not needed for your class.

The angle at the centre of a circle is twice the angle at the circumference when they are both subtended by the same arc. ① 180° in a triangle. 360° in a full turn. Base angles in isosceles triangles are equal.

① The angle at the centre of a circle is twice the angle at the circumference when they are both subtended by the same arc.

① The angle at the centre of a circle is twice the angle at the circumference when they are both subtended by the same arc.

① The angle at the centre of a circle is twice the angle at the circumference when they are both subtended by the same arc.

① The angle at the centre of a circle is twice the angle at the circumference when they are both subtended by the same arc.

① The angle at the centre of a circle is twice the angle at the circumference when they are both subtended by the same arc.

Every angle subtended at the circumference of a semicircle by the diameter is a right angle. ② 180° in a triangle. 360° in a full turn. Base angles in isosceles triangles are equal.

② ① Every angle subtended at the circumference of a semicircle by the diameter is a right angle. The angle at the centre of a circle is twice the angle at the circumference when they are both subtended by the same arc. ∴ If the angle at the centre is 180°, the angle at the circumference must be 90°.

② ① Every angle subtended at the circumference of a semicircle by the diameter is a right angle. The angle at the centre of a circle is twice the angle at the circumference when they are both subtended by the same arc. ∴ If the angle at the centre is 180°, the angle at the circumference must be 90°.

② Every angle subtended at the circumference of a semicircle by the diameter is a right angle.

③ ① Angles subtended at the circumference in the same segment of a circle are equal. The angle at the centre of a circle is twice the angle at the circumference when they are both subtended by the same arc. ∴ Angles – in the same segment – created from the same points are equal.

③ Angles subtended at the circumference in the same segment of a circle are equal.

Circle Theorems: Angles at the Circumference ① Conclusion: ② Conclusion: ③ Conclusion:

Circle Theorems: Angles at the Circumference ① Conclusion: ② ③ Conclusion: ③ Conclusion:

Circle Theorems: Angles at the Circumference ① The angle at the centre of a circle is twice the angle at the circumference when they are both subtended by the same arc. Conclusion: ② Every angle subtended at the circumference of a semicircle by the diameter is a right angle. Conclusion: ③ Conclusion: Angles subtended at the circumference in the same segment of a circle are equal.

Questions? Comments? Suggestions? …or have you found a mistake!? Any feedback would be appreciated . Please feel free to email: tom@goteachmaths. co. uk