Secant Lines
I CAN understand and apply theorems about circles including secant lines!
NC.M3.G-C.2 Understand and apply theorems about circles. Understand and apply theorems about relationships with angles and circles, including central, inscribed and circumscribed angles. Understand and apply theorems about relationships with line segments and circles including, radii, diameter, secants, tangents and chords.
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Angle Measures:�Interior Angle Theorem
Lesson 8-5: Angle Formulas
9
Angles that are formed by two intersecting chords.
The measure of the angle is the average of the intercepted arcs.
Interior Angle Theorem:
1
A
B
C
D
E
2
<AEC and <DEB are interior angles.
m<1 =m<2= mAC+mDB
2
Lesson 8-5: Angle Formulas
10
A
B
C
D
x°
91
85
Angle Measures
Example: Interior Angle Theorem
X=1/2 (mAC+mDB)
X=1/2 (91+85)
X= 88
*Do 23, 24, 25
Angle Measures
Example: Two Secants
Angle Measures
Find x: (120-50)/2 =35
*Do 26
Angle Measures: Secant & Tangent
Angle Measures: Secant & Tangent
Find A: ½ (60-20) =20
*Do 27
Angle Measures: Two tangents
Angle Measures: Two tangents
Find A= ½ (320-40)=280
*Do 28
320
Segment Lengths: Intersecting Interior Chords
Segment Lengths: Intersecting Interior Chords
Solve for x: (12)(6)=8x
72=8x
x=9
*Do 29, 30
Segment Lengths: Intersecting Secants
Segment Lengths: Intersecting Secants
Solve for x: 4(6+4)= 2(x+2)
4(10)=2x+4
40=2x+4
36=2x
x=18
*Do 31, 32, 33
Segment Lengths: Secant & Tangent
Segment Lengths: Secant & Tangent
Solve for x: x2=9(25)
x2=225
x=15
*Do 34, 35, 36
Vocabulary-fill out sheet
Summaries: also on back below work
Write a one sentence bullet point summary for each section you did today!
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Make sure:
Sectors Cornell notes has questions and summary
TOC is complete with all vocabulary
Math XLs are complete (5 total for this chapter)
The circus is in town...is it safe?
Page 31 in your workbook.
The circus has just arrived in town and is setting up. The fire code requires that they have at least 175 ft. of exterior walkways to pass inspection so that the audience members are safe. Use tangents to see if they are safe and if they will pass inspection!
Exit Ticket!
Create a question from the foldable sections you completed today!