NC.M2.G-SRT

NC.M2.G-SRT

NC.M2.G-SRT.1Verify experimentally the properties of dilations with given center and scale factor:NC.M2.G-SRT.12Develop properties of special right triangles (45-45-90 and 30-60-90) and use them to solve problems.NC.M2.G-SRT.1aWhen a line segment passes through the center of dilation, the line segment and its image lie on the same line. When a line segment does not pass through the center of dilation, the line segment and its image are parallel.NC.M2.G-SRT.1bThe length of the image of a line segment is equal to the length of the line segment multiplied by the scale factor.NC.M2.G-SRT.1cThe distance between the center of a dilation and any point on the image is equal to the scale factor multiplied by the distance between the dilation center and the corresponding point on the pre-image.NC.M2.G-SRT.1dDilations preserve angle measure.NC.M2.G-SRT.2Understand similarity in terms of transformations.NC.M2.G-SRT.2aDetermine whether two figures are similar by specifying a sequence of transformations that will transform one figure into the other.NC.M2.G-SRT.2bUse the properties of dilations to show that two triangles are similar when all corresponding pairs of sides are proportional and all corresponding pairs of angles are congruent.NC.M2.G-SRT.3Use transformations (rigid motions and dilations) to justify the AA criterion for triangle similarity.NC.M2.G-SRT.4Use similarity to solve problems and to prove theorems about triangles. Use theorems about triangles to prove relationships in geometric figures.NC.M2.G-SRT.4aA line parallel to one side of a triangle divides the other two sides proportionally and its converse.NC.M2.G-SRT.4bThe Pythagorean TheoremNC.M2.G-SRT.6Verify experimentally that the side ratios in similar right triangles are properties of the angle measures in the triangle, due to the preservation of angle measure in similarity. Use this discovery to develop definitions of the trigonometric ratios for acute angles.NC.M2.G-SRT.8Use trigonometric ratios and the Pythagorean Theorem to solve problems involving right triangles in terms of a context.
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