Look out for isosceles triangles and the angles in the same segment. Cyclic quadrilateral The angles that are either end of the diameter total 180o180o180o as if the triangle were a cyclic quadrilateral. They should total 90o90o90o as the angle in a semicircle is 90o90o90o. A ...
Image We know that each of the lines which is a radius of the circle (the green lines) are the same length. Therefore each of the two triangles is isosceles and has a pair of equal angles. Image But all of these angles together must add up to 180°, since they are the angles of ...
How to identify angles in the Circle theorems and the Alternate Segment Theorem? (Maths GCSE Revision) Show Step-by-step Solutions How to prove the Alternate Segment Theorem? Draw 3 radii from the center of the circle to the 3 points on the circle to form 3 isosceles triangles. ...
Because isosceles triangles have congruent base angles, mark ACD and ADC each as angle a, and ABD and ADB, each as angle b. The final angle in each triangle can be calculated using the triangle sum theorem: {eq}180 - 2a {/eq} and {eq}180 - 2b {/eq}. ...
polygon. I then derive two theorems about pairs of segments, that the reviser of the Ancient method should have known, that explain each method, why they work when they do and do not when they do not, and which lead to a curious generalization of the Revised method. Hero’s comment is...