Arcs and Angles Objective: Students will be able to apply past knowledge to solve problems involving arcs and angles with relationships to circles.

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Presentation transcript:

Arcs and Angles Objective: Students will be able to apply past knowledge to solve problems involving arcs and angles with relationships to circles.

Inscribed Angle The measure of an angle inscribed in a circle is one half the measure of the intercepted arc Angle COR = arc CR Angle CAR = ½ arc CR or ½ Angle COR

Inscribed Angles Intercepting the Same Arc Inscribed angles that intercept the same arc are congruent Angle PAQ and Angle PBQ both intercept arc PQ

Angles Inscribed in a Semicircle If the two chords of the angle have endpoints of the diameter then the angle is 90 degrees One side of the triangle formed is the diameter

Cyclic Quadrilaterals A quadrilateral inscribed in a circle All the vertices of the quad touch the circle The opposite angles of a cyclic quadrilateral are supplementary

Arcs By Parallel Lines A line that intersects a circle at 2 points is called a secant Secant passes through a circle and contains a chord How is this different than a tangent? Parallel Lines intercept congruent arcs in a circle

Examples

Examples

Proving Conjectures We did some of these in class Can you prove triangles congruent? Can you prove it is isosceles?

Examples

Example

Homework Pg 327 1,2,3,4,5,11 and 13 Honors 16 and 17 Pg 332 1 and 2