HG U6D3 Inscribed Polygons Oct31

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Angle Game: Find as many angles as you can.

Click on the link and explore.

www.geogebra.org/classic/nkwarEsv

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In the GeoGebra, move D around the circle. What changes?

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In the GeoGebra, move D around the circle. What stays the same?

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How do you locate the exact center of a circle?

The image shows a quadrilateral circumscribed by a circle.

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Highlight the arc from S to Q passing through P.

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The image shows a quadrilateral circumscribed by a circle.

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Highlight the arc from S to Q passing through P.

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The image shows a quadrilateral circumscribed by a circle.

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Highlight the arc from S to Q passing through P.

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Explore

Can you construct a circle to inscribe the quadrilateral?

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Click on the link and try it.

www.geogebra.org/classic/zykxkj5c

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A quadrilateral ABCD has the given angle measures. Select all measurements which could come from a cyclic quadrilateral.

angle A is 70^o, angle B is 110^o, angle C is 70^o, and angle D is 110^o

angle A is 90^o, angle B is 90^o, angle C is 90^o, and angle D is 90^o

angle A is 50^o, angle B is 40^o, angle C is 120^o, and angle D is 150^o

angle A is 80^o, angle B is 80^o, angle C is 100^o, and angle D is 100^o

angle A is 60^o, angle B is 50^o, angle C is 120^o, and angle D is 130^o

Quadrilateral ABCD is cyclic with given angle measures.

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Use the figure to solve for x and y.

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Do you agree with Lin? Explain or show your reasoning.

Use the figure to solve for x, y and z.

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Use the figure to solve for x and y.

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In the diagram, the measure of angle ACB is 43 degrees.

What is the measure of angle AOB?

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Which statement must be true?

A chord is a diameter.

A diameter is a chord.

A chord is a radius.

A central angle’s vertex is on the circle.

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HG U6D3 Inscribed Polygons Oct31

Angle Game: Find as many angles as you can.

In the GeoGebra, move D around the circle. What changes?

In the GeoGebra, move D around the circle. What stays the same?

How do you locate the exact center of a circle?

Highlight the arc from S to Q passing through P.

Highlight the arc from S to Q passing through P.

Highlight the arc from S to Q passing through P.

A quadrilateral ABCD has the given angle measures. Select all measurements which could come from a cyclic quadrilateral.

Do you agree with Lin? Explain or show your reasoning.

Which statement must be true?

A circle and line are drawn.
How many intersection points are possible? Select all possible answers.

Angle Game: Find as many angles as you can.

In the GeoGebra, move D around the circle. What changes?

In the GeoGebra, move D around the circle. What stays the same?

How do you locate the exact center of a circle?

Highlight the arc from S to Q passing through P.

Highlight the arc from S to Q passing through P.

Highlight the arc from S to Q passing through P.

A quadrilateral ABCD has the given angle measures. Select all measurements which could come from a cyclic quadrilateral.

Do you agree with Lin? Explain or show your reasoning.

Which statement must be true?

A circle and line are drawn.
How many intersection points are possible? Select all possible answers.

HG U6D3 Inscribed Polygons Oct31

HG U6D3 Inscribed Polygons Oct31

Angle Game: Find as many angles as you can.

In the GeoGebra, move D around the circle. What changes?

In the GeoGebra, move D around the circle. What stays the same?

How do you locate the exact center of a circle?

Highlight the arc from S to Q passing through P.

Highlight the arc from S to Q passing through P.

Highlight the arc from S to Q passing through P.

A quadrilateral ABCD has the given angle measures. Select all measurements which could come from a cyclic quadrilateral.

Do you agree with Lin? Explain or show your reasoning.

Which statement must be true?

A circle and line are drawn. How many intersection points are possible? Select all possible answers.

Angle Game: Find as many angles as you can.

In the GeoGebra, move D around the circle. What changes?

In the GeoGebra, move D around the circle. What stays the same?

How do you locate the exact center of a circle?

Highlight the arc from S to Q passing through P.

Highlight the arc from S to Q passing through P.

Highlight the arc from S to Q passing through P.

A quadrilateral ABCD has the given angle measures. Select all measurements which could come from a cyclic quadrilateral.

Do you agree with Lin? Explain or show your reasoning.

Which statement must be true?

A circle and line are drawn. How many intersection points are possible? Select all possible answers.

A circle and line are drawn.
How many intersection points are possible? Select all possible answers.

A circle and line are drawn.
How many intersection points are possible? Select all possible answers.