Page 161 - Math Course 3 (Book 2)

Circles: Arcs and Chords

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Answer

Prove Theorem 11.2
Statements Reasons
PROOF
1. DE ≅ FG; m∠EBF = 24; Choose the best reason to complete the following
DFG is a semicircle. 1. Given proof.
Given: AB ≅ EF
2. mDFG = 180 2. Def. of semicircle
AB ≅ CD
3. In a circle, if 2
3. DE ≅ FG chords are ≅, corr. Prove: CD ≅ EF
minor arcs are ≅.
A B
4. mDE = mFG 4. Def. of ≅ arcs
C F
5. Def. of arc
5. mEF = 24
measure
6. Arc Addition
6. mED + mEF + mFG = mDFG
Postulate
E D
7. mFG + 24 + mFG = 180 7. Substitution

8. Subtraction
8. 2(mFG) = 156 Property and Statements Reasons
simplify 1. AB ≅ EF; AB ≅ CD 1. Given
9. mFG = 78 9. Division Property 2. In a circle, 2 minor
2. AB ≅ EF arcs are ≅, chords are ≅
10. Def. of arc
10. mFG = m∠FBG
measure 3. CD ≅ EF 3. ___________
11. m∠FBG = 78 11. Substitution. 4. In a circle, 2 chords
4. CD ≅ EF
are ≅, minor arcs are ≅.
A. Segment Addition Postulate
B. Definition of ≅
Standardized text Example C. Definition of Chord
D. Transitive Property
A regular hexagon is drawn in a circle as part of a
logo for an advertisement. If opposite vertices are Answer
connected by line segments, what is the measure
of angle P in degrees? Standardized text Example

A ADVERTISING
A logo for an advertising campaign is a pentagon
that has five congruent central angles. Determine
P whether A
B
A. yes
B. no Z P
C. cannot be determined

Since connecting the opposite vertices of a regular
hexagon divides the hexagon into six congruent S T
triangles, each central angle will be congruent. The
measure of each angle is 360 ÷ 6 or 60.

Answer 60 Answer

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