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March 27, 2014 11.1 Similar Polygons Congruent Polygon - Hexagon ABCDEF is similar to Hexagon PQRSTU Similar Polygon - Ratio Proportion March 27, 2014 March 27, 2014 Transformations rigid - non-rigid - March 27, 2014 y 6 4 2 -6 -4 -2 2 4 6 x -2 -4 -6 C-92 Dilation Similarity Conjecture If one polygon is the image of another polygon under a dilation then the polygons are similar. March 27, 2014 11.2 Similar Triangles Shortcuts: Congruences Similarity What needs to be true for triangles to be similar? Look for counterexamples March 27, 2014 Two congruent angles C-93 AA Similarity Conjecture If two angles of one triangle are congruent to two angles of another triangle then the triangles are similar. March 27, 2014 March 27, 2014 Two sides in proportion March 27, 2014 Three sides in proportion C-94 SSS Similarity Conjecture If the three sides of one triangle are proportional to the three sides of another triangle, then the two triangles are similar. March 27, 2014 Two sides in proportion and a congruent angle included angle adjacent angle C-95 SAS Similarity Conjecture If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent; triangles are similar. March 27, 2014 * Go through estimating the height of the ceiling using a mirror Lynda is standing 4 ft behind a fence 6.5ft. tall. When she looks over the fence, she can just see the top edge of a building. She knows that the building is 32.5ft behind the fence. Her eyes are 5 ft from the ground. How tall is the building? You need to add 5 supports under a ramp, in addition to a 3.6m one at the end, so that they are all equally spaced. How long should each support be? Driving through the mountains, Jon has to go up and over a high mountain pass. The road has a constant incline for 7.75 miles to the top of the pass. Jon notices from a road sign that in the first mile he climbs 840 feet. What is the height of the mountain pass? March 27, 2014 y 6 4 2 -6 -4 -2 2 -2 -4 -6 4 6 x March 27, 2014 y 6 4 2 -6 -4 -2 2 -2 -4 -6 4 6 x