Illustrative Mathematics - Geometry - Unit 7 - Lesson 4 - Formative Library | Library

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

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

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

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

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

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

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Lin is looking at cyclic quadrilateral ABCD. She says, “I’m not convinced that opposite angles of cyclic quadrilaterals always add up to 180 degrees. For example, in this diagram, suppose we moved point A to a different spot on the circle. Angle BCD would still measure 100 degrees, but now angle BAD would have a different measure, and they wouldn’t add up to 180.”

Do you agree with Lin? Explain or show your reasoning

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Line AC is tangent to the circle centered at O with radius 3 units. The length of segment AC is 4.5 units. 
Find the length of segment AB.

3+\sqrt{29.25} units

\sqrt{29.25} units

-3 +\sqrt{29.25} units

26.25

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In the diagram, the measure of angle ACB is 25 degrees.
 What is the measure of angle AOB?

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Which statement must be true?

A chord is a radius.

A diameter is a chord.

A chord is a diameter.

A central angle’s vertex is on the circle.

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

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This lesson is from Illustrative Mathematics. Geometry, Unit 7, Lesson 4. Internet. Available from https://curriculum.illustrativemathematics.org/HS/teachers/2/7/4/index.html ; accessed 29/July/2021.

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