3.3 CPCTC and Circles
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Transcript of 3.3 CPCTC and Circles
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3.3 CPCTC and Circles
By: Josie LaCoe andSarah Parkinson
Period 1
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CPCTC=
CorrespondingParts ofCongruentTriangles areCongruent
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Explanation of CPCTC
If two triangles are congruent, then all of the corresponding parts of those two triangles are congruent.
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Explanation of CPCTC
This means that if COW PIG, then and CO PI. This is also true for all other corresponding parts of the triangles.
PC
W
O
C P
I
G
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Circles!!!
Point W is the center of this circle. All circles are named by their center, so this circle would be called circle W or O W.
.W
.
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Circles!!!
A circle is made up of only the outer edge, not the center.
.WCircle (rim)
Center of circle (Not a part of the circle)
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Circles!!!
Since all of points of a circle are the same distance from the center…
THEOREM 19!!!!-All radii of a circle are congruent!
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Review Formulas
Although you probably know these formulas from previous math classes, here’s just a little refresher:
A= r C=2 r 2
3.141592654
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Sample Problem #1
Given: OSProve: IE JO
Statements Reasons
1. OS 1. Given
2. SJ SO SI SE 2.All radii of a O are
3. JSO ISE 3. Vertical s are
4. JSO ISE 4. SAS (2,2,3)
5. IE JO 5. CPCTC
.
J
O
S
I
E
.
.
Solution:
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Sample Problem #2
Given: OJFind the perimeter of SJP
Solution:SJ and PJ=1/2 PRSJ and PJ=1/2(12)SJ and PJ=6PS=7Perimeter of SJP=
6+6+7=19
7
12
S
JP
R
.
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Practice Problem #1
Given: E A B is the mdpt of AE
Prove: C D
A
B
C
D E
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Practice Problem #2
a. Find the coordinates of point Sb. Find the circumference of the circle
(Round to the nearest tenth)
.(107, 59)
.S
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Practice Problem Solutions
1. Statements Reasons
1. E A 1. Given
2. B is mdpt of AE 2. Given
3. AB BE 3. Mdpt seg into 2 segs
4. ABC EBD 4. Vertical s are
5. ABC EBD 5. ASA (1, 3,4)
6. C D 6. CPCTC
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Practice Problem Solutions
2a. The coordinates of the center of the circle is (107, 59) (107 being the x-coordinate and 59, the y-coordinate). This means the x-coordinate of S is 107 and since S is on the x-axis, the y-coordinate is 0, making the coordinates of S (107,0)
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Practice Problem Solutions
2b. C=2 r C=2 59
C 370.7
Because the y-coordinate (the distance from the x-axis to the point) of the center of the circle is 59, this is also the radius of the circle (the distance from the center of a circle to the outside edge). This number is plugged into the equation and the equation is solved for C.
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Works Cited
Rhoad Richard, George Milauskas, Robert Whipple. Geometry for Enjoyment and Challenge. Illinois: McDougal Littell, 1997. Print.