Similar Polygons /Dilations

Similar Polygons Corresponding angles are congruent. Corresponding sides are proportional Corresponding angles are congruent. Which means what about the overall shape of the figure? Same SHAPE, different SIZE

Example ABCD ~ TPOR Similarity Statement: Identifies similar polygons and corresponding parts Just like when congruent, order is given in the statement ~ means similar Key to Solving: Find the Scale Factor Scale Factor: Corresponding sides in the figure that both have a measurement

What is the scale factor from TPOR to ABCD? Ratio Denominator Numerator

Solve for Missing Sides: Set up proportions, be consistent (sides are proportional when similar) Follow ABCD to TPOR Solve for z Solve for X Scale Factor Solve for y Z is an angle. Angles are CONGRUENT 5x = 24 x = 4.8 40 = 3z-20 60 = 3z 20 = z 25 = 3y 8.3 = y

ABC ~ EDC ALWAYS RE-DRAW if corresponding parts are not matched up Solve for x, y and z

Warm-up Find x, y, and z

A dilation is a transformation that changes the size of a figure but not its shape. The pre-image and the image are always similar shapes. A scale factor for a dilation with a center at the origin is k, which is found by multiplying each coordinate by k: (a, b)  (ka, kb).

A (1,4) A ‘ (2,8) B (5,1) B ‘(10,2) C (0,0) C ‘ ( 0,0) Given Triangle ABC, graph the image Of ABC with a scale factor of 2. (2x, 2y) Pre-Image Image A (1,4) A ‘ (2,8) B (5,1) B ‘(10,2) C (0,0) C ‘ ( 0,0)

Triangle ABC has vertices A ( 0,0) , B( 4,0) , C (0,5). Graph it If the coordinates of each vertex of ABC are increased by 2, will the new triangle be similar to triangle ABC (Graph it)? Why or why not? 2) If the coordinates of each vertex of Triangle ABC are multiplied by 2, will the new triangle be similar to Triangle ABC (Graph it)? Why or why not?