geometry section 10-3 1112
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Section 10-3Arcs and Chords
Monday, May 14, 2012
Essential Questions
• How do you recognize and use relationships between arcs and chords?
• How do you recognize and use relationships between arcs, chords, and diameters?
Monday, May 14, 2012
Theorems10.2 - Congruent Minor Arcs:
10.3 - Perpendicularity:
10.4 - Perpendicularity:
10.5 - Congruent Chords:
Monday, May 14, 2012
Theorems10.2 - Congruent Minor Arcs: In the same or congruent
circles, two minor arcs are congruent IFF their corresponding chords are congruent
10.3 - Perpendicularity:
10.4 - Perpendicularity:
10.5 - Congruent Chords:
Monday, May 14, 2012
Theorems10.2 - Congruent Minor Arcs: In the same or congruent
circles, two minor arcs are congruent IFF their corresponding chords are congruent
10.3 - Perpendicularity: If a diameter or radius of a circle is perpendicular to a chord, then it bisects the chord and its arc
10.4 - Perpendicularity:
10.5 - Congruent Chords:
Monday, May 14, 2012
Theorems10.2 - Congruent Minor Arcs: In the same or congruent
circles, two minor arcs are congruent IFF their corresponding chords are congruent
10.3 - Perpendicularity: If a diameter or radius of a circle is perpendicular to a chord, then it bisects the chord and its arc
10.4 - Perpendicularity: The perpendicular bisector of a chord is a diameter or radius of the circle
10.5 - Congruent Chords:
Monday, May 14, 2012
Theorems10.2 - Congruent Minor Arcs: In the same or congruent
circles, two minor arcs are congruent IFF their corresponding chords are congruent
10.3 - Perpendicularity: If a diameter or radius of a circle is perpendicular to a chord, then it bisects the chord and its arc
10.4 - Perpendicularity: The perpendicular bisector of a chord is a diameter or radius of the circle
10.5 - Congruent Chords: In the same or congruent circles, two chords are congruent IFF they are equidistant from the center
Monday, May 14, 2012
Example 1 In X , AB ≅ CD and mCD = 90°. Find mAB .
Monday, May 14, 2012
Example 1 In X , AB ≅ CD and mCD = 90°. Find mAB .
mAB = 90°
Monday, May 14, 2012
Example 2 In the figure, A ≅ B and WX ≅ YZ . Find WX .
Monday, May 14, 2012
Example 2 In the figure, A ≅ B and WX ≅ YZ . Find WX .
7x − 2 = 5x + 6
Monday, May 14, 2012
Example 2 In the figure, A ≅ B and WX ≅ YZ . Find WX .
7x − 2 = 5x + 6
2x = 8
Monday, May 14, 2012
Example 2 In the figure, A ≅ B and WX ≅ YZ . Find WX .
7x − 2 = 5x + 6
2x = 8
x = 4
Monday, May 14, 2012
Example 2 In the figure, A ≅ B and WX ≅ YZ . Find WX .
7x − 2 = 5x + 6
2x = 8
x = 4
WX = 7(4) − 2
Monday, May 14, 2012
Example 2 In the figure, A ≅ B and WX ≅ YZ . Find WX .
7x − 2 = 5x + 6
2x = 8
x = 4
WX = 7(4) − 2
WX = 28 − 2
Monday, May 14, 2012
Example 2 In the figure, A ≅ B and WX ≅ YZ . Find WX .
7x − 2 = 5x + 6
2x = 8
x = 4
WX = 7(4) − 2
WX = 28 − 2
WX = 26Monday, May 14, 2012
Example 3 In G, mDEF =150°. Find mDE.
Monday, May 14, 2012
Example 3 In G, mDEF =150°. Find mDE.
mDE =
12
mDEF
Monday, May 14, 2012
Example 3 In G, mDEF =150°. Find mDE.
mDE =
12
mDEF
mDE =
12
(150)
Monday, May 14, 2012
Example 3 In G, mDEF =150°. Find mDE.
mDE =
12
mDEF
mDE =
12
(150)
mDE = 75°
Monday, May 14, 2012
Example 4 In C , AB =18 inches and EF = 8 inches. Find CD.
Monday, May 14, 2012
Example 4 In C , AB =18 inches and EF = 8 inches. Find CD.
CF is a radius.
Monday, May 14, 2012
Example 4 In C , AB =18 inches and EF = 8 inches. Find CD.
CF is a radius.
a2 + b2 = c2
Monday, May 14, 2012
Example 4 In C , AB =18 inches and EF = 8 inches. Find CD.
CF is a radius.
a2 + b2 = c2
42 + b2 = 92
Monday, May 14, 2012
Example 4 In C , AB =18 inches and EF = 8 inches. Find CD.
CF is a radius.
a2 + b2 = c2
42 + b2 = 92
16 + b2 = 81
Monday, May 14, 2012
Example 4 In C , AB =18 inches and EF = 8 inches. Find CD.
CF is a radius.
a2 + b2 = c2
42 + b2 = 92
16 + b2 = 81
b2 = 65
Monday, May 14, 2012
Example 4 In C , AB =18 inches and EF = 8 inches. Find CD.
CF is a radius.
a2 + b2 = c2
42 + b2 = 92
16 + b2 = 81
b2 = 65
b = 65
Monday, May 14, 2012
Example 4 In C , AB =18 inches and EF = 8 inches. Find CD.
CF is a radius.
a2 + b2 = c2
42 + b2 = 92
16 + b2 = 81
b2 = 65
b = 65 inches or ≈ 8.06 inches
Monday, May 14, 2012
Example 5 In P , EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ.
Monday, May 14, 2012
Example 5 In P , EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ.
4x − 3 = 2x + 3
Monday, May 14, 2012
Example 5 In P , EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ.
4x − 3 = 2x + 3
2x = 6
Monday, May 14, 2012
Example 5 In P , EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ.
4x − 3 = 2x + 3
2x = 6
x = 3
Monday, May 14, 2012
Example 5 In P , EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ.
4x − 3 = 2x + 3
2x = 6
x = 3
PQ = 4(3) − 3
Monday, May 14, 2012
Example 5 In P , EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ.
4x − 3 = 2x + 3
2x = 6
x = 3
PQ = 4(3) − 3
PQ = 12 − 3
Monday, May 14, 2012
Example 5 In P , EF = GH = 24, PQ = 4x − 3, and PR = 2x + 3. Find PQ.
4x − 3 = 2x + 3
2x = 6
x = 3
PQ = 4(3) − 3
PQ = 12 − 3
PQ = 9
Monday, May 14, 2012
Check Your Understanding
p. 704 #1 - 6
Monday, May 14, 2012
Problem Set
Monday, May 14, 2012
Problem Set
p. 705 #7-33 odd, 45, 49, 51
"I may not have gone where I intended to go, but I think I have ended up where I needed to be." - Douglas Adams
Monday, May 14, 2012
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