6.4 Use Inscribed Angles and Polygons Quiz: Friday

Vocabulary An inscribed angle is an angle whose vertex is on the circle and whose sides contain chords of the circle.

Vocabulary The arc that lies in the interior of an inscribed angles and has endpoints on the angle is called the intercepted arc of the angle.

Vocabulary Measure of an Inscribed Angle Theorem –the measure of an inscribed angle is one half the measure of its intercepted arc. 50 o A B C 100 o

Vocabulary Theorem 6.10 –If two inscribed angles of a circle intercept the same arc, then the angles are congruent.

Vocabulary A polygon is an inscribed polygon if all of its vertices lie on a circle. The circle that contains the vertices is a circumscribed circle. –Remember: a polygon is a closed figure made up of 3 or more straight lines.

Vocabulary Theorem 6.11 –If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle.

Vocabulary Theorem 6.12 –A quadrilateral (4-sided figure) can be inscribed in a circle if and only if its opposite angles are supplementary (add up to be 180 o ) 90 O

Example: Find the indicated measure in circle P. a) angle Sb) arc RQ

You Try:

Example: Find the value of each variable.

You Try: Find the values of a and b.

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