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Analytic Geometry - EOCT REVIEW 1
January 7-10
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A dilation is a transformation that makes a figure larger or
smaller than the original figure based on a ratio given by a
scale factor. When the scale factor is greater than 1, the
figure is made larger. When the scale factor is between 0
and 1, the figure is made smaller. When the scale factor is
1, the figure is the same.
When a figure is transformed under a dilation: the
corresponding angles of the pre-image and the image are
congruent: the corresponding sides of the pre-image and
the image are proportional: and the pre-image and image
are similar.
Draw a triangle with vertices at A(0,1), B(-3,3), and
C(1,3), Dilate the triangle using a scale factor of 1.5 and
a center of (0, 0). Name the dilated triangle A'B'C^' _
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Line segment CD is 5 inches long. If line segment CD is
dilated to fonn line segment CD' with a scale factor of 0.6,
what is the length of line segment CD'?
CDIf = C'D'
5{.6) = 3
CD' = 3 inches
Figure A'B'C'D' is a dilation of figure ABCD.
a. (4,2)
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DC
b. AB/f = A'B'
12fc = 6
'
k=V2
Q
a. Determine the center of dilation.
b. Determine the scale factor of the dilation.
c. What is the relationship between the sides of the pre-image and
corresponding sides of the image?
c. The sides of the pre-image and the corresponding
sides of the image are proportional.
Analytic Geometry - EOCT REVIEW 2
January 13-17
Rectangle WXYZ has coordinates W(1,2), X(3, 2),
Y(3, -3), and Z(1,-3).
a. Graph the image of rectangle WXYZ after a rotation of
90° clocl<wise about the origin. Label the image W'X'Y'Z'.
b. Translate rectangle W'X'Y'Z' 2 units left and 3 units up.
c. Is rectangle WXYZ congruent to rectangle W"X"Y"Z"?
Explain.
Yes. Rotations and translations are congruence
transformations.
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UJ
Define and illustrate the (3) ways to prove triangle similarity.
AA - If two angles of one triangle are congruent to two
angles of another triangle, then the triangles are similar.
SSS - If the three sides of one triangle are proportional
to the three corresponding sides of another triangle,
then the triangles are similar.
SAS - If two sides of one triangle are proportional to
two sides of another triangle and their included angles
are congruent, then the triangles are similar.
Define and illustrate
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a. Alternate Interior Angles Theorem - If two parallel lines
are cut by a transversal, then the alternate interior
angles formed by the transversal are congruent.
W
2'
Y
r
AAfiC - A O f f
C^ASC ~ ADEF
AASC ~ A D f f
h. Corresponding Angles Postulate - If two parallel lines
are cut by a transversal, then the corresponding angles
formed by the transversal are congruent.
z l = z3, z 2 = z 4 , z 5 s z 7 , z 6 = z 8
c. Vertical Angles Thm - Vertical angles are congruent.
z l = z2
Define and illustrate
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a. Triangle Angle-Sum Theorem - The sum of the
measures of the angles of a triangle is 180°.
b. Isosceles Triangle Theorem - If two sides of a triangle
are congruent, then the angles opposite those sides are
also congruent.
A
mZi4 + mZB + mZC = 180'
zs ^ zc
c. the Triangle Sum Theorem.
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DC
Define and illustrate centroid. Explain the properties of a
centroid.
Centroid - the point of concurrency of the three medians
of a triangle.
Properties of a centroid:
•
The center of gravity of the triangle.
•
The centroid is located two-thirds of the
distance from each vertex to the midpoint of
the opposite side.