"9A" 1/04/09

Today in our class we started off by getting our quiz back and answering the

questions people had problems with. After we checked our quizzes Mrs. Saatkamp taught us four new theorems that are: theorem 9-4, theorem 9-5, theorem 9-6 and theorem 9-7. All of these theorems talked about INSCRIBED ANGLES. The definition for inscribed angles is an angle which vertex is ON the circle.

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Theorem 9-4: -If an angle is inscribed in a circle

-Then the measure of the angle equals ½ the measure of the intersected arc.

Example:

Since angle EDF vertex's is on the circle the angle is a inscribed angle therefore angle EDF is 1/2 of arc CE

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Theorem 9-5: - If 2 inscribed angles of a circle or congruent circles intercept congruent arcs of the same arc

-Then the angles are congruent.

Examples:

In the first circle(to the left) both inscribed angles, angle BCD and angle DEB, share the same arc the angles are congruent.

In the second circle they DON'T share the same arc, but both arcs are congruent since the arcs are congruent so are the angles.

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Theorem 9-6: -If an inscribed angle of a circle intercepts a semicircle

-Then the angle is a right one.

Example:

Arc BC is a semicircle measuring 180º and angle BDC is a inscribed angle. Angle BDC is a right angle. This can be proven with the formula used in theorem 9-4 of angle= 1/2 of arc.

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Theore 9-7: -If a QUADRILATERAL is inscribed in a circle

-Then its opposite angles are supplementary.

Example:

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After we finished with the theorems Mrs. Saatkamp gave us work to do which was page. 470, questions 17-45 (ALL). Whoever didn’t finish had to do it for homework since we are going to check it tomorrow in class.

see you tomorrow :)

happy april's fools

malena