In geometry, each step needs a reason. Use the standard wording: the angle at the center is twice the angle at the circumference; angles in the same segment are equal; the angle in a semicircle is 90°; opposite angles of a cyclic quadrilateral add to 180°.
Combine these with older facts such as angles in a triangle add to 180° and base angles of an isosceles triangle are equal. Triangles formed by two radii are isosceles, which often unlocks a problem.
Worked example
AB is a diameter and C is on the circle. Why is ∠ACB = 90°?
- AB passes through the center.
- C stands on the semicircle.
Answer:The angle in a semicircle is 90°.
Key words
- reason
- the fact that justifies a step
- isosceles triangle
- two equal sides, two equal angles
- diameter
- a chord through the center
Practise this
New questions every time.
Common Core-referenced: HSG-C.A.2