inscribed angles section 10-4. inscribed angle – an angle whose vertex is on the circle and whose...

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Inscribed Angles Section 10- 4

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Page 1: Inscribed Angles Section 10-4. inscribed angle – an angle whose vertex is on the circle and whose sides each contain chords of the circle. ADC is an inscribed

Inscribed Angles

Section 10-4

Page 2: Inscribed Angles Section 10-4. inscribed angle – an angle whose vertex is on the circle and whose sides each contain chords of the circle. ADC is an inscribed

inscribed angle – an angle whose vertex is on the circle and whose sides each contain chords of the circle.

ADC is an inscribed arc.

A

BC

D

.angleinscribedanisABC

Page 3: Inscribed Angles Section 10-4. inscribed angle – an angle whose vertex is on the circle and whose sides each contain chords of the circle. ADC is an inscribed

Inscribed Angle Thm (10.5)

If an angle is inscribed in a circle, then the measure of the angle equals ½ the measure of its intercepted arc.

70o

140o

Page 4: Inscribed Angles Section 10-4. inscribed angle – an angle whose vertex is on the circle and whose sides each contain chords of the circle. ADC is an inscribed

Theorem 10.6

If 2 inscribed angles of a circle or congruent circles intercept congruent arcs or the same arc, then the angles are congruent.

A

BC

D ABCADC

Page 5: Inscribed Angles Section 10-4. inscribed angle – an angle whose vertex is on the circle and whose sides each contain chords of the circle. ADC is an inscribed

Theorem 10.7

If an inscribed angle of a circle intercepts a semicircle, then the angle is a right angle.

180o

Page 6: Inscribed Angles Section 10-4. inscribed angle – an angle whose vertex is on the circle and whose sides each contain chords of the circle. ADC is an inscribed

Theorem 10.8

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

60o

120o

Page 7: Inscribed Angles Section 10-4. inscribed angle – an angle whose vertex is on the circle and whose sides each contain chords of the circle. ADC is an inscribed

Joke Time

What do you get if you take a native Alaskan and divide its circumference by its diameter?

Eskimo pi

Page 8: Inscribed Angles Section 10-4. inscribed angle – an angle whose vertex is on the circle and whose sides each contain chords of the circle. ADC is an inscribed

Why did Humpty Dumpty have a great fall?

To make up for his miserable summer