10.4 Inscribed Angles. Open a new geogebra file 1)Construct a circle A. 2)Place a point C on the circle such that arc BC is a minor arc. 3)Find the measure.

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Presentation transcript:

10.4 Inscribed Angles

Open a new geogebra file 1)Construct a circle A. 2)Place a point C on the circle such that arc BC is a minor arc. 3)Find the measure of angle BAC. 4)Place a point D on the circle such that arc BDC is a major arc. 5)Compare the two angles and make a conjecture. 6)Adjust point C, is your conjecture still true?

Inscribed Angles An inscribed angle has its vertex on the circle and its sides are chords Has half the measure of its corresponding arc. Inscribed AnglesNot Inscribed Angles

Geogebra 1)Construct a Circle A with points B, C, D and E on the circle. 2)Construct quadrilateral BCDE. 3)Find the measure of each angle. 4)What do you notice about their measures? 5)What do inscribed angles have to do with what you discovered in step (4)?

Opposite Angles in an Inscribed Quadrilateral are supplementary.

Geogebra 1)Construct a circle A. 2)Place points B, C and D on the circle such that BC is a minor arc and BDC is a major arc. 3)Place point E on major arc BDC. 4)Find the measures of inscribed angles BDC and BEC. 5)What do you notice? Why does this happen?

Geogebra 1)Construct a circle A. 2)Construct a diameter BC. 3)Inscribe three angles intercepting semicircle BC. 4)What do you notice about their measures? Why does this happen?

Angles inscribed in a semicircle are Right Angles.

Guided Practice