Lesson 11.1 ADV: 1.Homework Discussion 2.Similar Polygons 3.Dilations

Warm Up:

Difference between Congruent and Similar: Congruent: figures that have the same size and shape. Similar: figures that have the same shape, but not necessarily the same size.

Polygon/Circle Similarity: Are all equilateral triangles similar? Are all squares similar? Are all rectangles similar? Are all circles similar? How would you identify congruent circles?

Characteristics of Similar Polygons: Investigation #1: Use patty paper to complete investigation #1 Summary of Similar Polygons: Similar Polygons must have: 1) 2)

Example #1: Are the Polygons Similar? Explain. a) b)

Example #1: Are the Polygons Similar? c)

Similarity Statement: If we are given that these 2 polygons are similar, we know that: Corresponding angles are congruent: Corresponding segments are proportional: Therefore, the similarity statement is:

Example #2: Determine the values of x and y given that the triangles are similar.

Investigation #2: Dilation is an enlargement or a reduction of a figure that maintains shape. This is a NON-RIGID transformation. The scale factor describes how we enlarge or reduce the figure. Multiply each coordinate by the scale factor to get the image. The scale factor is represented by the letter k. Dilation Similarity Conjecture: If one polygon is a dilated image of another polygon, then _____________________________________.

Example #3: On your own graph paper, determine the coordinates of the image after using the scale factor to create the dilation.

Homework: P : 4, 8-10, 12-14, 16, 18, 22