Presentation on theme: "Introduction Recognizing and using congruent and similar shapes can make calculations and design work easier. For instance, in the design at the corner,"— Presentation transcript:
2 IntroductionRecognizing and using congruent and similar shapes can make calculations and design work easier. For instance, in the design at the corner, only two different shapes were actually drawn. The design was put together by copying and manipulating these shapes to produce versions of them of different sizes and in different positions.
3 Similar and Congruent Figures Congruent triangles have all sides congruent and all angles congruent.Similar triangles have the same shape; they may or may not have the same size.
4 Similar and Congruent Figures Note: Two figures can be similar but not congruent, but they can’t be congruent but not similar. Think about why!
5 ExamplesThese figures are similar and congruent. They’re the same shape and size.Symbolized by ≅
6 Ratios and Similar Figures Similar figures have corresponding sides and corresponding angles that are located at the same place on the figures.Corresponding sides have to have the same ratios between the two figures.A ratio is a comparison between 2 numbers (usually shown as a fraction)
7 Ratios and Similar Figures BEFExampleGHCDThese angles correspond:A and EB and FD and HC and GThese sides correspond:AB and EFBD and FHCD and GHAC and EG
8 Ratios and Similar Figures ExampleThese rectangles are similar, because the ratios of these corresponding sides are equal:
9 Proportions and Similar Figures A proportion is an equation that states that two ratios are equal.Examples:n = m = 4
10 Proportions and Similar Figures You can use proportions of corresponding sides to figure out unknown lengths of sides of polygons.16 m10 mn5 m
11 Proportions and Similar Figures You can use proportions of corresponding sides to figure out unknown lengths of sides of polygons.16 m10 mn5 m
12 Similar triangles Similar triangles are triangles with the same shape For two similar triangles,corresponding angles have the same measurelength of corresponding sides have the same ratio65o25oA4 cm2cm12cmBExampleAngle A = 90oSide B = 6 cm
13 Proportions and Similar Figures Can you solve for the missing variable in these similar triangles?12J2012
14 PRACTICE PROBLEMS Ratio and proportion review Page 581 #1, 2, 6-13 Similar polygon problems Page 591 #12-19