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Analytic Geometry - EOCT REVIEW 1 January 7-10 1 1 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^' _ o S 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) en 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. o 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 O CO 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 I 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. I 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.