PPT-ALGEBRA I @ SECTION 2-8 : PROPORTIONS and SIMILAR FIGURES

1 A sailboat and its model are shown at the right What is the length of the model sailboat 18 feet 25 feet 10 f t ANSWER 72 feet SIMILAR FIGURES have the same shape though not necessarily the same size . What are similar polygons?. Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional.. Congruent Figures. In order to be congruent, two figures must be the same size and same shape.. as part of the development of the “Math 5: Geometry” curriculum for Arizona State University’s Teaching Foundations Project. . AMP 2012-2013: . Saturday #2. What are we doing here?. Too much math never killed anyone.. Objectives. Learn to . write and solve problems using proportions. . Proportions. Proportions are frequently used to solve problems in mathematics.. Proportional reasoning can be applied in many situations, including reading and drawing maps, architecture, and construction. . Ch. 2 Lesson 3. Pg. 123. What will you will learn?. Enlarge Photographs. Make something from a pattern. Identify Similarity. Two figures are . similar. if the second can be obtained from the first by a sequence of transformations and dilations. . Pythagoras (560-480 BC), the Greek geometer, was especially interested in the golden section, and proved that it was the basis for the proportions of the human figure. He showed that the human body is built with each part in a definite golden proportion to all the other parts.. Proportions. What are proportions?. - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures.. What do we mean by similar?. - Similar describes things which have the same shape but are not the same size.. What are similar polygons?. Two polygons are similar if corresponding (matching) angles are congruent and the lengths of corresponding sides are proportional.. Congruent Figures. In order to be congruent, two figures must be the same size and same shape.. 7.4 Similar Figures. Vocabulary. corresponding sides. corresponding angles. similar. Matching sides of two or more polygons are called . corresponding sides,. and matching angles are called . corresponding angles. (Not exactly the same, but pretty close!). Let’s do a little review work before discussing similar figures.. Congruent Figures. In order to be congruent, two figures must be the same size and same shape.. Section 2-8. Goals. Goal. To find missing lengths in similar figures.. To use similar figures when measuring indirectly.. Rubric. Level 1 – Know the goals.. Level 2 – Fully understand the goals.. 1) A sailboat and its model are shown at the right. What is the length of the model sailboat?. 18 feet. 25 feet. ??. 10. f. t.. ANSWER : 7.2 feet. SIMILAR FIGURES :. . have the same shape, though not necessarily the same size. . Similar Figures Similar Similar figures have the same shape, but not necessarily the same size. Similar Polygons 14 m 7m 60° 60° The ratio formed by the sides is the scale factor : 14m = 2m Proportions and Similar Figures What is Similarity? Not Similar Similar Similar Not Similar Similar Triangles Similar Figures Figures that have the same shape but not necessarily the same size are Near-Duplicate Figures. Thanawin. (Art) . Rakthanmanon. Qiang. Zhu. Eamonn. Keogh. What is a near-duplicate pattern?. A History of . Infusoria. , including . Desmidiaceae. and . Diatomaceae. , 1861..