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Cyclic Quadrilaterals Worksheet

Explore the properties of cyclic quadrilaterals, including opposite angles, exterior angles, and related theorems, with this Grade 10 math worksheet.

Grade 10 Math GeometryCyclic Quadrilateral
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Includes

Multiple Choice2 Short AnswerFill in the BlanksTrue / False

Standards

CCSS.MATH.CONTENT.HSG.C.A.3CCSS.MATH.CONTENT.HSG.C.A.2
7 sections · Free to use · Printable
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Cyclic Quadrilaterals

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. Which of the following statements is true about a cyclic quadrilateral?

a

All sides are equal.

b

Opposite angles are supplementary.

c

Diagonals are perpendicular.

d

All angles are right angles.

2. In the cyclic quadrilateral ABCD shown below, if ∠A = 80° and ∠B = 110°, find the measures of ∠C and ∠D.

ABCD80°110°

∠C =  

∠D =  

3. The exterior angle of a cyclic quadrilateral is equal to the   interior opposite angle.

4. A quadrilateral can be cyclic if and only if the perpendicular bisectors of its sides are  .

5. All rectangles are cyclic quadrilaterals.

T

True

F

False

6. A rhombus is always a cyclic quadrilateral.

T

True

F

False

7. A cyclic quadrilateral has angles (2x + 10)°, (3x - 20)°, (y + 30)°, and (2y - 10)°. Find the values of x and y.