Angles in the Same Segment Flashcards

All 4 cards in this deck

State the circle theorem about angles in the same segment.

Angles in the same segment, subtended by the same arc (chord), are equal.

Which angle equals $\angle ACB$ by 'angles in the same segment'?

e.g. chord $AB$, with $C$ and $D$ both on the major arc

$\angle ADB$ — angles in the same segment are equal, so $\angle ADB = \angle ACB$.

True or false? Two angles at the circumference in the same segment are equal even if they stand on different chords.

False. They must be subtended by the same chord (arc).

True or false? An angle in the major segment equals the angle in the minor segment standing on the same chord.

False. Those two angles sum to $180^\circ$ (opposite angles of a cyclic quadrilateral).