12-2 Chords and Arcstafths.org/ourpages/auto/2016/1/21/53285260/12-2.pdf2016/01/21 ·...
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Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved. Vocabulary Review Chapter 12 318 Chords and Arcs 12-2 Circle the converse of each statement. 1. Statement: If I am happy, then I sing. If I sing, then I am happy. If I am not happy, then I do not sing. If I do not sing, then I am not happy. 2. Statement: If parallel lines are cut by a transversal, then alternate interior angles are congruent. If lines cut by a transversal If lines cut by a transversal If lines cut by a transversal form are not parallel, then form alternate interior alternate interior angles that are alternate interior angles angles that are not congruent, then the lines are are not congruent. congruent, then the parallel. lines are not parallel. Vocabulary Builder chord (noun) kawrd Definition: A chord is a segment whose endpoints are on a circle. Related Word: arc Use Your Vocabulary 3. Complete each statement with always, sometimes, or never. A chord is 9 a diameter. A diameter is 9 a chord. A radius is 9 a chord. A chord 9 has a related arc. An arc is 9 a semicircle. chord RS R O S
Transcript of 12-2 Chords and Arcstafths.org/ourpages/auto/2016/1/21/53285260/12-2.pdf2016/01/21 ·...
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Chapter 12 318
Chords and Arcs12-2
Circle the converse of each statement.
1. Statement: If I am happy, then I sing.
If I sing, then I am happy. If I am not happy, then I do not sing.
If I do not sing, then I am not happy.
2. Statement: If parallel lines are cut by a transversal, then alternate interior angles are congruent.
If lines cut by a transversal If lines cut by a transversal If lines cut by a transversal form are not parallel, then form alternate interior alternate interior angles that are alternate interior angles angles that are not congruent, then the lines are are not congruent. congruent, then the parallel. lines are not parallel.
Vocabulary Builder
chord (noun) kawrd
Definition: A chord is a segment whose endpoints are on a circle.
Related Word: arc
Use Your Vocabulary
3. Complete each statement with always, sometimes, or never.
A chord is 9 a diameter.
A diameter is 9 a chord.
A radius is 9 a chord.
A chord 9 has a related arc.
An arc is 9 a semicircle.
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O
S
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d. Problem 1
Theorem 12-4 Within a circle or in congruent circles, congruent central angles have congruent arcs.
4. If /AOB > , then AB0
> CD0
.
Converse Within a circle or in congruent circles, congruent arcs have congruent central angles.
5. If AB0
> CD0
, then /AOB > .
Theorem 12-5 Within a circle or in congruent circles, congruent central angles have congruent chords.
6. If /AOB > /COD, then AB > .
Converse Within a circle or in congruent circles, congruent chords have congruent central angles.
7. If AB > CD, then > /COD.
Theorem 12-6 Within a circle or in congruent circles, congruent chords have congruent arcs.
8. If AB > , then AB0
> CD0
.
Converse Within a circle or in congruent circles, congruent arcs have congruent chords.
9. If AB0
> , then AB > CD.
Theorems 12-4, 12-5, 12-6 and Their Converses
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BC ≅BC ≅
Theorem 12-4 Theorem 12-5
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⊙O ≅ ⊙P
Given
GivenIsosceles △ Theorem
Transitive Property Corresponding parts of ≅ △’s are ≅.
∠B ≅
∠C ≅
≅ OB ≅ ≅
and ∠D ≅ ∠B ≅
≅ circles have ≅ radii.
△BCO ≅ △
∠O ≅
AAS
319 Lesson 12-2
Using Congruent Chords
Got It? Use the diagram at the right. Suppose you are given (O O (P and lOBC O lPDF . How can you show lO O lP? From this, what else can you conclude?
10. Complete the flow chart below to explain your conclusions.
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Problem 2
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Chapter 12 320
Finding the Length of a Chord
Got It? What is the value of x? Justify your answer.
16. What is the measure of each chord? Explain.
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17. Circle the reason why the chords are congruent.
Chords that have equal Chords that are equidistant from measures are congruent. the center of a circle are congruent.
18. Circle the theorem that you will use to find the value of x.
Theorem 12-5 Theorem 12-7 Converse of Theorem 12-7
Theorem 12-8 Theorem 12-10
19. Circle the distances from the center of a circle to the chords.
16 18 36 x
20. The value of x is .
Theorem 12-7 Within a circle or in congruent circles, chords equidistant from the center or centers are congruent.
Converse Within a circle or in congruent circles, congruent chords are equidistant from the center (or centers).
11. If OE 5 OF, then AB > .
12. If AB > , then OE 5 .
Theorem 12-8 In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc.
13. If AB is a diameter and AB ' CD, then CE > and CA0
> .
Theorem 12-9 In a circle, if a diameter bisects a chord (that is not a diameter), then it is perpendicular to the chord.
14. If AB is a diameter and CE > ED, then AB ' .
Theorem 12-10 In a circle, the perpendicular bisector of a chord contains the center of the circle.
15. If AB is the perpendicular bisector of chord CD, then contains the center of (O.
Theorem 12-7 and Its Converse, Theorems 12-8, 12-9, 12-10
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Now Iget it!
Need toreview
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Math Success
Problem 3
Problem 4
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321 Lesson 12-2
Vocabulary Is a radius a chord? Is a diameter a chord? Explain your answers.
27. Circle the name(s) of figure(s) that have two endpoints on a circle. Underline the name(s) of figure(s) that have one endpoint on a circle.
chord diameter radius ray segment
28. Is a radius a chord? Is a diameter a chord? Explain.
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• Do you UNDERSTAND?
Check off the vocabulary words that you understand.
circle chord radius diameter
Rate how well you can use chords to find measures.
Using Diameters and Chords
Got It? The diagram shows the tracing of a quarter. What is its radius?
Underline the correct word to complete each sentence. Then do each step.
21. First draw two chords / tangents .
22. Next construct one / two perpendicular bisector(s).
23. Label the intersection C. It is the circle’s center / chord .
24. Measure the diameter / radius . 25. The radius is about mm.
Finding Measures in a Circle
Got It? Reasoning In finding y, how does the auxiliary BA make the problem simpler to solve?
26. BA is the hypotenuse of a right 9, so you can use the 9 Theorem to solve for y.
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