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Review from Sec. 11.2
Central angle of a circle …
- vertex lies on the center of the circle
- formed by two radii of the circle
- measure of the central angle equals the measure of its intercepted minor arc
Notes from Sec. 11.4
Triangle inscribed in a circle …
- When a triangle is inscribed in a circle, all of its vertices lie on the circle.
- The sides of the triangle are chords of the circle.
Triangle circumscribed about/around a circle …
- When a triangle is circumscribed about a circle, then the sides of the triangle are
tangents of the circle.
- The radius drawn to the point of tangency must be perpendicular to the sides of
the triangle.
Inscribed angle of a circle …
- vertex lies on the circle
- formed by two chords of the circle
- measure of an inscribed angle equals one-half the measure of its intercepted arc
Thm: If an angle is inscribed in a semicircle, then the angle is a right angle.
Proof … If the angle is inscribed in a semicircle, then its intercepted arc is the other semicircle
… since the measure of a semicircle is always 180 degrees, the measure of the angle will
always be 1/2 (180) or 90 degrees
Thm: If a quadrilateral is inscribed in a circle, then its opposite angles must be supplementary.
Proof … The opposite angles of the quadrilateral intercept two arcs that cover the entire circle
… since the two arcs cover the entire circle, their measures sum to 360 degrees
… since the opposite angles are inscribed, their measures equal ½ their intercepted arcs
… the sum of the opposite angles = ½ (sum of the intercepted arcs) = ½ (360) = 180
… sum of the measures of the opposite angles = 180, the angles are supplementary
HW for Tuesday: Read through Sec. 11.4 and WATCH lesson videos, as needed.
Complete pg. 776 -777 #12 – 20