Transcript Angles Measures & Segment Lengths Ch. 11.4

EOC REVIEW #5
Monday
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Find the volume of the figure.
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Now, find the surface area.
(Hint: Find the slant height of the pyramid.)
10 class days till EOC! 
Warm Up Reflections over
Vertical Lines
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1) Plot A(3,4) and reflect over x=5.
2) Plot B(8,2) and reflect over x=5.
3) Plot C(5,2) and reflect over x=9 and
then over x=1. Find C’’.
4) Pl(-1,3) and reflect over x=-1.
REMINDER
Can you find a …
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Radius
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Diameter
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Tangent
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Chord
REMINDER
Central Angles
Inscribed Angles
The measure of an angle formed by a tangent and a
chord is half the measure of the intercepted arc.
ACUTE angle
OBTUSE angle
Examples:
ACUTE angle
OBTUSE angle
Checkpoint Quiz #1
Use your notes!!
1. 52 in.
2. 44 cm
3. 40 m
4. 6
5. 12
6.
7.
8.
9.
11.5
x = 37, y = 100
x = 116, y =88, z = 79
x = 120
Angle Measures and
Segment Lengths
Ch. 11.4 Toolkit
Today’s Goal(s):
1.
To find the measures of angles formed
by chords, secants, and tangents.
2.
To find the lengths of segments
associated with circles.
A secant is a line, ray, or segment
that intersects a circle at two points.
How do I find the measure of an angle
formed by two lines that intersect:
INSIDE a circle?
Ex.1: Add the arcs & divide by two.
How do I find the measure of an angle
formed by two lines that intersect:
OUTSIDE a circle?
Ex.2: Subtract the arcs & divide by two.
How do I find the lengths of segments
formed by two lines that intersect?
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For a given point and circle, the product of the lengths
of the two segments from the point to the circle is the
same along any line through the point and circle.
Ex.1: Two chords
Always start at the point of intersection!
Ex.2: Two secants
Always start at the point of intersection!
Ex.3: Secant & tangent
Always start at the point of intersection!
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The tangent segment counts twice!
Photography
You focus your camera on a fountain. Your camera
is at the vertex of the angle formed by tangents to
the fountain. You estimate that this angle is 40.
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What is the measure of the arc of
the circular basin of the fountain
that will be in the photograph?
Bridge Design
The arch of the Taiko Bashi is an arc of a
circle. A 14-ft chord is 4.8 ft from the edge of
the circle. Find the radius of the circle.
You Try…
(continue with previous classwork)
Geometry Book pg. 611
 #’s 7 and 15
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