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Name: ________________________ Class: ___________________ Date: __________ ID: A 11.2 Chords & Central Angles Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. In the diagram below, circle O has a radius of 5, and CE = 2. Diameter AC is perpendicular to chord BD at E. What is the length of BD ? a. 12 b. 10 ____ c. d. 8 4 2. The circle graph shows the colors of automobiles sold at a car dealership. Find mCD. a. mCD = 36° c. mCD = 170° b. mCD = 10° d. mCD = 20° 1 Name: ________________________ ____ ____ ID: A 3. Find mCFB. a. mCFB = 130° c. mCFB = 230° b. mCFB = 140° d. mCFB = 90° 4. WX ≅ YZ . Find mWX . a. mWX = 17° c. mWX = 1° b. mWX = 5° d. mWX = 23° 2 ID: A 11.2 Chords & Central Angles Quiz Answer Section MULTIPLE CHOICE 1. ANS: C Because OC is a radius, its length is 5. Since CE = 2 OE = 3. BD = 8 . PTS: 2 2. ANS: A mCD = m∠CPD mCD = 0.10(360°) REF: fall0811ge STA: G.G.49 EDO is a 3-4-5 triangle. If ED = 4, TOP: Chords Theorem: The measure of a minor arc is equal to the measure of its central angle. m∠CPD is 10% of 360°. mCD = 36° Feedback A B C D Correct! The measure of a minor arc is equal to the measure of its central angle. The measure of a minor arc is equal to the measure of its central angle. The measure of a minor arc is equal to the measure of its central angle. PTS: OBJ: TOP: DOK: 1 DIF: Average 11-2.1 Application 11-2 Arcs and Chords DOK 2 REF: 1cd5521a-4683-11df-9c7d-001185f0d2ea LOC: MTH.C.11.03.05.03.02.006 KEY: arc measure | circle graph | central angle 1 ID: A 3. ANS: A m∠BPD = 50° mBD = 50° m∠CPF = m∠FPD = 90° mCF = mFD = 90° m∠FPD = m∠FPB + m∠BPD 90° = m∠FPB + 50° m∠FPD = 40° Vertical Angle Theorem m∠BPD = 50° Definition of perpendicular lines m∠CPF = m∠FPD = 90° mFB = 40° Angle Addition Postulate Substitute. Simplify. m∠FPD = 40° mCFB = mCF + mFB Arc Addition Postulate mCFB = 90° + 40° = 130° Substitute. Feedback A B C D Correct! Add the measure of arc CF and the measure of arc FB. Add the measure of arc CF and the measure of arc FB. Add the measure of arc CF and the measure of arc FB. PTS: OBJ: TOP: DOK: 4. ANS: 1 DIF: Average REF: 1cd5792a-4683-11df-9c7d-001185f0d2ea 11-2.2 Using the Arc Addition Postulate LOC: MTH.C.11.03.05.03.02.005 11-2 Arcs and Chords KEY: arc measure | arc addition postulate DOK 2 A Congruent chords have congruent arcs. mWX = mYZ 3x + 2 = 4x − 3 Substitute the given measures. 2= x−3 Subtract 3x from both sides. 5=x Add 3 to both sides. Substitute 5 for x and simplify. mWX = 3(5) + 2 = 17° Feedback A B C D Correct! This is x. Now solve for the arc length. Set the two expressions equal to each other and solve. Congruent chords have congruent arcs. PTS: OBJ: STA: LOC: KEY: 1 DIF: Average REF: 1cd7b476-4683-11df-9c7d-001185f0d2ea 11-2.3 Applying Congruent Angles, Arcs, and Chords NY.NYLES.MTH.05.GEO.G.G.49.a MTH.C.11.03.05.03.02.006 | MTH.C.11.03.05.04.005 TOP: 11-2 Arcs and Chords chord | arc measure DOK: DOK 2 2 Name: ________________________ Class: ___________________ Date: __________ ID: B 11.2 Chords & Central Angles Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ 1. WX ≅ YZ . Find mWX . a. mWX = 5° c. mWX = 17° b. mWX = 23° d. mWX = 1° 2. In the diagram below, circle O has a radius of 5, and CE = 2. Diameter AC is perpendicular to chord BD at E. What is the length of BD ? a. 10 b. 12 c. d. 1 4 8 Name: ________________________ ____ ____ ID: B 3. The circle graph shows the colors of automobiles sold at a car dealership. Find mCD. a. mCD = 170° c. mCD = 10° b. mCD = 20° d. mCD = 36° 4. Find mCFB. a. mCFB = 140° c. mCFB = 90° b. mCFB = 130° d. mCFB = 230° 2 ID: B 11.2 Chords & Central Angles Quiz Answer Section MULTIPLE CHOICE 1. ANS: C Congruent chords have congruent arcs. mWX = mYZ 3x + 2 = 4x − 3 2= x−3 5=x mWX = 3(5) + 2 = 17° Substitute the given measures. Subtract 3x from both sides. Add 3 to both sides. Substitute 5 for x and simplify. Feedback A B C D This is x. Now solve for the arc length. Congruent chords have congruent arcs. Correct! Set the two expressions equal to each other and solve. PTS: 1 DIF: Average REF: 1cd7b476-4683-11df-9c7d-001185f0d2ea OBJ: 11-2.3 Applying Congruent Angles, Arcs, and Chords STA: NY.NYLES.MTH.05.GEO.G.G.49.a LOC: MTH.C.11.03.05.03.02.006 | MTH.C.11.03.05.04.005 TOP: 11-2 Arcs and Chords KEY: chord | arc measure DOK: DOK 2 2. ANS: D Because OC is a radius, its length is 5. Since CE = 2 OE = 3. EDO is a 3-4-5 triangle. If ED = 4, BD = 8 . PTS: 2 REF: fall0811ge STA: G.G.49 1 TOP: Chords ID: B 3. ANS: D mCD = m∠CPD mCD = 0.10(360°) Theorem: The measure of a minor arc is equal to the measure of its central angle. m∠CPD is 10% of 360°. mCD = 36° Feedback A B C D The measure of a minor arc is equal to the measure of its central angle. The measure of a minor arc is equal to the measure of its central angle. The measure of a minor arc is equal to the measure of its central angle. Correct! PTS: 1 DIF: Average OBJ: 11-2.1 Application TOP: 11-2 Arcs and Chords DOK: DOK 2 4. ANS: B m∠BPD = 50° mBD = 50° m∠CPF = m∠FPD = 90° mCF = mFD = 90° m∠FPD = m∠FPB + m∠BPD 90° = m∠FPB + 50° m∠FPD = 40° REF: 1cd5521a-4683-11df-9c7d-001185f0d2ea LOC: MTH.C.11.03.05.03.02.006 KEY: arc measure | circle graph | central angle Vertical Angle Theorem m∠BPD = 50° Definition of perpendicular lines m∠CPF = m∠FPD = 90° mFB = 40° Angle Addition Postulate Substitute. Simplify. m∠FPD = 40° mCFB = mCF + mFB Arc Addition Postulate mCFB = 90° + 40° = 130° Substitute. Feedback A B C D Add the measure of arc CF and the measure of arc FB. Correct! Add the measure of arc CF and the measure of arc FB. Add the measure of arc CF and the measure of arc FB. PTS: OBJ: TOP: DOK: 1 DIF: Average REF: 1cd5792a-4683-11df-9c7d-001185f0d2ea 11-2.2 Using the Arc Addition Postulate LOC: MTH.C.11.03.05.03.02.005 11-2 Arcs and Chords KEY: arc measure | arc addition postulate DOK 2 2 Name: ________________________ Class: ___________________ Date: __________ 11.2 Chords & Central Angles Quiz Multiple Choice Identify the choice that best completes the statement or answers the question. ____ ____ 1. The circle graph shows the colors of automobiles sold at a car dealership. Find mCD. a. mCD = 20° c. mCD = 10° b. mCD = 36° d. mCD = 170° 2. WX ≅ YZ . Find mWX . a. mWX = 23° c. mWX = 17° b. mWX = 1° d. mWX = 5° 1 ID: C Name: ________________________ ____ ____ ID: C 3. Find mCFB. a. mCFB = 130° c. mCFB = 90° b. mCFB = 140° d. mCFB = 230° 4. In the diagram below, circle O has a radius of 5, and CE = 2. Diameter AC is perpendicular to chord BD at E. What is the length of BD ? a. 4 b. 10 c. d. 2 8 12 ID: C 11.2 Chords & Central Angles Quiz Answer Section MULTIPLE CHOICE 1. ANS: B mCD = m∠CPD mCD = 0.10(360°) Theorem: The measure of a minor arc is equal to the measure of its central angle. m∠CPD is 10% of 360°. mCD = 36° Feedback A B C D The measure of a minor arc is equal to the measure of its central angle. Correct! The measure of a minor arc is equal to the measure of its central angle. The measure of a minor arc is equal to the measure of its central angle. PTS: OBJ: TOP: DOK: 2. ANS: 1 DIF: Average REF: 1cd5521a-4683-11df-9c7d-001185f0d2ea 11-2.1 Application LOC: MTH.C.11.03.05.03.02.006 11-2 Arcs and Chords KEY: arc measure | circle graph | central angle DOK 2 C Congruent chords have congruent arcs. mWX = mYZ 3x + 2 = 4x − 3 Substitute the given measures. 2= x−3 Subtract 3x from both sides. 5=x Add 3 to both sides. Substitute 5 for x and simplify. mWX = 3(5) + 2 = 17° Feedback A B C D Congruent chords have congruent arcs. Set the two expressions equal to each other and solve. Correct! This is x. Now solve for the arc length. PTS: OBJ: STA: LOC: KEY: 1 DIF: Average REF: 1cd7b476-4683-11df-9c7d-001185f0d2ea 11-2.3 Applying Congruent Angles, Arcs, and Chords NY.NYLES.MTH.05.GEO.G.G.49.a MTH.C.11.03.05.03.02.006 | MTH.C.11.03.05.04.005 TOP: 11-2 Arcs and Chords chord | arc measure DOK: DOK 2 1 ID: C 3. ANS: A m∠BPD = 50° mBD = 50° m∠CPF = m∠FPD = 90° mCF = mFD = 90° m∠FPD = m∠FPB + m∠BPD 90° = m∠FPB + 50° m∠FPD = 40° Vertical Angle Theorem m∠BPD = 50° Definition of perpendicular lines m∠CPF = m∠FPD = 90° mFB = 40° Angle Addition Postulate Substitute. Simplify. m∠FPD = 40° mCFB = mCF + mFB Arc Addition Postulate mCFB = 90° + 40° = 130° Substitute. Feedback A B C D Correct! Add the measure of arc CF and the measure of arc FB. Add the measure of arc CF and the measure of arc FB. Add the measure of arc CF and the measure of arc FB. PTS: 1 DIF: Average REF: 1cd5792a-4683-11df-9c7d-001185f0d2ea OBJ: 11-2.2 Using the Arc Addition Postulate LOC: MTH.C.11.03.05.03.02.005 TOP: 11-2 Arcs and Chords KEY: arc measure | arc addition postulate DOK: DOK 2 4. ANS: C Because OC is a radius, its length is 5. Since CE = 2 OE = 3. EDO is a 3-4-5 triangle. If ED = 4, BD = 8 . PTS: 2 REF: fall0811ge STA: G.G.49 2 TOP: Chords