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7.2: Similar Polygons

7.2: Similar Polygons . p. 346-353. Similar Polygons. 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

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7.2: Similar Polygons

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  1. 7.2: Similar Polygons p. 346-353

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

  3. 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

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

  5. 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

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

  7. Warm-up Find x, y, and z

  8. A dilationis 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 factorfor a dilation with a center at the origin is k, which is found by multiplying each coordinate by k: (a, b)  (ka, kb).

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

  10. 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?

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