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Aim: What are Similar Polygons? What is a Scale Factor or Ratio of Similitude? Do Now: What is ratio of the length of picture A to the length of picture B Download Sketch 48 and fill in the accompanying worksheet. Big Sara smiles The lengths and widths of the pictures are in the same ratio. Little Sara smiles ~ Aim: Similarity Similar corresponding, comparable, Course: Applied Geo. alike ~ Aim: What are Similar Polygons? What is a Scale Factor or Ratio of Similitude? Do Now: What is ratio of the length of picture A to the length of picture B length A 10" 2 length B 5" 1 width A 4" 2 width B 2" 1 Similarly, find the ratio of the width of picture A with the width of picture B A 10” The lengths and widths of the pictures are in the same ratio. ~ B corresponding, 5” comparable, Course: Applied Geo. Aim: Similarity 4” Similar - alike 2” ~ Ratio compares 2 numbers by division the ratio 1 to 4 is written 1 : 4 or 1/4 the ratio 4 : 1 is not the same as 1 : 4 other ratios equal to 1/4 are found by multiplying numerator and denominator by the same factor Ex. 1 6 6 4 6 24 Reduce a ratio: divide numerator and denominator by greatest common factor Ex. Aim: Similarity 6 6 1 24 6 4 Course: Applied Geo. Proportion An equation that says two ratios are equivalent (equal). In a proportion, the product of the means is equal to the product of the extremes MEAN EXTREME 1 3 2 6 MEAN This proportion reads, “1 is to 2 as 3 is to 6” EXTREME Cross Products: 1 6 = 2 Property of Proportion If two ratios form a proportion, then the cross products are equal. If the cross products of two ratios are Course: Applied Geo. Aim: Similarity equal, then the ratios form a proportion. Are dimensions of corresponding parts for polygons in column A & column B in the same ratio? A A No B = 5 4 V = 5 1 5 1 S 4 DC = VU 4 1 4 1 DC VU B AD SV 5 C A Yes = 5 1 5 1 5 D 5 D 4 AD SV C 3 S B T 5 4 U T 5 V 4 U HOW DO THE TWO PAIRS COMPARE? Can you say either pair ofCourse: Applied Geo. polygons is similar to each other? Aim: Similarity What does similar mean? What does similarity mean in geometry? How do we define precisely what are properties of similar figures? •Are corresponding parts congruent? •Are corresponding angles congruent? •Do the shapes look alike? •Can they look different? Explain what you think is meant by similar geometric shapes. Aim: Similarity Course: Applied Geo. 1. Similar polygons are two polygons in which the A) corresponding sides are in proportion and the B) corresponding angles are congruent. A) Corresponding sides are in proportion 2 1 Ratio of Similitude B) Corresponding angles are congruent The scale factor comparing two corresponding sides of similar polygons is also called the ratio of similitude Aim: Similarity Note: Similar Polygons haveCourse: theApplied Geo. same shape, but are of different size Quadrilateral 1 ~ Quadrilateral 2. Find the value of the variables. 6 4 1 9 y z x 2 12 15 Recall: All corresponding sides of similar polygons are in proportion: the ratio of similitude or scale factor What is the ratio of similitude for these figures? 6 y Aim: Similarity 9 12 y=8 6 4 9 x x=6 6 9 6 z Course: Applied Geo. 9 15 z = 10