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How does a dilation centered at the origin with scale factor k change a point?Dilations: Multiply both coordinates by k: (x, y) → (kx, ky).
A point moves from (2,3) to (6,9) under a dilation centered at the origin. What is the scale factor?Dilations: 3, because each coordinate is multiplied by 3.
How does a dilation differ from a rigid motion?Dilations: A dilation keeps angle measures but changes lengths unless the scale factor is 1, so the image is similar, not necessarily congruent.
What is true about corresponding parts of similar polygons?Similar Polygons: Corresponding angles are congruent, and corresponding sides are proportional by one scale factor.
How do you write a similarity ratio?Similar Polygons: Pair up sides that occupy the same places on the two shapes, then divide in the same order each time.
If the side lengths of a figure are multiplied by k, how do its perimeter and area change?Similar Polygons: The perimeter is multiplied by k and the area by k². For example, doubling sides doubles perimeter and quadruples area.
What does the AA Similarity criterion say?Triangle Similarity: If two angles of one triangle are congruent to two angles of another, the triangles are similar.
What does the SAS Similarity criterion require?Triangle Similarity: Two pairs of sides are proportional and the included angles are congruent.
What does the SSS Similarity criterion require?Triangle Similarity: All three pairs of corresponding sides are proportional with the same scale factor.
What does the Triangle Proportionality Theorem say?Proportional Segments: A line parallel to one side of a triangle divides the other two sides proportionally.
How do three or more parallel lines divide two transversals?Proportional Segments: They divide the transversals proportionally.
How do you set up a proportion to find a missing segment length?Proportional Segments: Write a proportion with corresponding pieces across from each other, then solve for the missing length.
How can similar triangles and shadows find the height of a tall object?Applications of Similarity: Compare a small object and its shadow with a taller object and its shadow, provided the sun angle is the same.
How do you use a scale drawing to find real lengths?Applications of Similarity: A scale drawing is a mini version of the real thing. Use the same conversion for every length.
What happens when you draw the altitude to the hypotenuse of a right triangle?Applications of Similarity: It creates two smaller right triangles that are similar to the original triangle and to each other.