OpenRevise

Flashcards · Maths · Circle Theorems

Same Segment and Cyclic Quadrilaterals

16 cards

  1. What is a segment of a circle?

    The part of a circle cut off by a chord.

  2. What is true of angles in the same segment?

    They are equal.

  3. What must be true of two angles for the same-segment theorem?

    They are made by the same chord, on the same side.

  4. What is a cyclic quadrilateral?

    A quadrilateral with all four corners on a circle.

  5. What do opposite angles of a cyclic quadrilateral add up to?

    \(180^\circ\).

  6. If one angle of a cyclic quadrilateral is \(74^\circ\), what is the opposite angle?

    \(106^\circ\).

  7. What is the reason for opposite angles of a cyclic quadrilateral?

    Opposite angles of a cyclic quadrilateral add up to \(180^\circ\).

  8. What is an exterior angle of a cyclic quadrilateral equal to?

    The interior opposite angle.

  9. What do the four angles of a quadrilateral add up to?

    \(360^\circ\).

  10. What do you do when angles are given as expressions?

    Form an equation, using the theorem, and solve it.

  11. Which pairs of angles are opposite in \(ABCD\)?

    \(A\) and \(C\), and \(B\) and \(D\).

  12. Can two angles on opposite sides of a chord be equal?

    Not by the same-segment theorem; they add up to \(180^\circ\) instead.

  13. What is the first step in a circle theorem problem?

    Decide which theorem each angle belongs to.

  14. What should you write on the diagram?

    Every angle you find.

  15. Is a rectangle a cyclic quadrilateral?

    Yes, its opposite angles add up to \(180^\circ\).

  16. Is a parallelogram that is not a rectangle cyclic?

    No.