Congruent Chords and Arcs Worksheet

This worksheet focuses on understanding and applying theorems related to congruent chords and arcs in circles for Grade 10 Geometry students.

Grade 10 Math GeometryCongruent Chords and Arcs

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Includes

Multiple ChoiceFill in the BlanksShort AnswerTrue / FalseLong Answer

Standards

CCSS.MATH.CONTENT.HSG.C.A.2CCSS.MATH.CONTENT.HSG.C.A.3

Topics

GeometryCirclesChordsArcsCongruence

7 sections · Free to use · Printable

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Congruent Chords and Arcs

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

1. In a circle, if two chords are congruent, then their corresponding minor arcs are:

Proportional

Congruent

Supplementary

Complementary

2. If a diameter is perpendicular to a chord, then it bisects the chord and its arc. This statement is:

Always True

Sometimes True

Never True

Cannot be determined

3. If two chords in a circle are equidistant from the center, then the chords are .

4. A chord is a segment whose endpoints lie on the of a circle.

5. In circle O, if chord AB is congruent to chord CD, and the measure of arc AB is 70 degrees, what is the measure of arc CD?

6. A chord has a length of 16 cm and is 6 cm from the center of the circle. What is the radius of the circle?

7. If two chords in a circle are congruent, then their corresponding central angles are not necessarily congruent.

True

False

8. In the same circle or in congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

True

False

9. In a circle with center O, chords PQ and RS are congruent. If the distance from O to PQ is 5 units, and the radius of the circle is 13 units, find the length of chord RS. Explain your reasoning.