UNIT 5
STANDARDS:
G.SRT.A.1a - Verify experimentally the properties of dilations given by a center and a scale factor: a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
G.GPE.B.6 - Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
G.SRT.A.1b - Verify experimentally the properties of dilations given by a center and a scale factor: the dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.B.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
G.SRT.A.2 - Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G.SRT.A.3 - Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
LEARNING TARGETS:
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5.1: To perform dilations given a center and scale factor, labeling the preimage, A, and its image, A'.
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5.2: To understand that the line connecting a preimage to its image will pass through the center of dilation.
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5.3: To understand that a ratio (slope of a line) can be used to partition a segment.
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5.4: To find the point that partitions a segment into a given ratio.
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5.5: To understand that when a line or segment is dilated, the preimage and image are parallel.
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5.6: To understand that when a line passes through the center of dilation, the preimage and image of that line are the same.
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5.7: To determine the scale factor of a dilation, given preimage and its image.
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5.8: To dilate an image using a variety of scale factors, including negative and fractional factors.
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5.9: To understand that dilations preserve corresponding angle measures in its preimage and its image.
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5.10: To understand that dilations create proportional corresponding side lengths in its preimage and its image.
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5.11: To define similarity using dilations.
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5.12: To know that all similar figures maintain congruent corresponding angles and proportional corresponding sides.
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5.13: To discover the minimum requirements to prove triangles are similar using dilations.
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5.14: To prove triangles are similar using AA (Angle-Angle) similarity criterion, including congruent triangles.