GeometrySection 10-4

Use Inscribed Angles and Polygons

Inscribed Angles

An angle whose vertex is on a circle and whose sides contain chords of the circle

Intercepted arc is the arc that has the endpoints on the angle

Measure of an Inscribed Angle

The measure of an inscribed angle is one half the measure of its intercepted arc.

Congruent Inscribed Angles Theorem

If two inscribed angles of a circle intercepts the same arc, then the angles are congruent

Inscribed Polygons

All the vertices lie on a circle

The circle that contains the vertices is a circumscribed circle

Inscribed Right Angle Theorem

If a right angle is inscribed in a circle, then the hypotenuse is a diameter of a circle.

Also, if one side of an inscribed angle is the diameter, then the triangle is a right triangle, with the right angle opposite the diameter

Inscribed Quadrilateral Theorem

A quadrilateral can be inscribed in a circle iff its opposite angles are supplementary

Examples

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Assignment

Section 10-4Page 676Problems # 4-24 evens