Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Click the mouse button or press the Space Bar to display the answers. Objective Identify similar polygons and find missing measures of similar polygons Vocabulary Polygon A simple closed figure in a plane formed by three or more line segments Vocabulary Similar Polygons that have the same shape Is similar to Vocabulary Corresponding parts Parts of a similar figure that “match” Vocabulary Congruent Parts of a geometric figure that have the same measure is congruent to Vocabulary Scale factor A ratio of the lengths of two corresponding sides of two similar polygons Math Symbols angle Math Symbols Segment AB AB Measure of AB AB Example 1 Identify Similar Polygons Example 2 Find Missing Measures Example 3 Scale Factor and Perimeter Determine whether triangle DEF is similar to triangle HJK. Explain your reasoning. First, check to see if corresponding angles are congruent. and 1/3 Next, check to see if corresponding sides are proportional. Change ratio to decimal Compare the decimals Answer: Angles are equal and ratios of sides are equal so triangles are similar 1/3 Determine whether triangle ABC is similar to triangle TRI. Explain your reasoning. T A C B I R Answer: Yes; corresponding angles are congruent and 1/3 Given that rectangle GHIJ ~ rectangle LMNO, write a proportion to find the measure of Then solve. Small rectangle Large rectangle 2 3 x Define a variable for measure of NO Write a proportion of the rectangles from known similar sides 2/3 x Small rectangle Large rectangle 4 n Write a proportion of the rectangles from a known similar sides with the unknown “n” 2/3 Write a proportion using the 2 ratios 2 4 = 3 x Cross multiply Bring down = Bring down 2x = 2x = 3(4) Multiply 3 4 2x = 12 Ask “what is being done to the variable?” The variable is being multiplied by 2 Do the inverse on both sides of the = sign 2/3 Do the inverse on both sides of the = sign 2 4 = 3 x Bring down 2x = 12 2x = 3(4) Using the fraction bar, divide both sides by 2 Combine “like” terms 2x = 12 Bring down = 2x = 12 2 2 Combine “like” terms 1x = 6 x = 6 Use the Identify Property to multiply 1x Bring down = 6 Answer: Measure of NO = 6 Find the measure of 2/3 Given that rectangle ABCD ~ rectangle WXYZ, write a proportion to find the measure of Then solve. Answer: = 15 2/3 MULTIPLE- CHOICE TEST ITEM A polygon has sides 2.5 times as long as a similar polygon. The smaller polygon has a perimeter of 42 inches inches. What is the perimeter of the larger polygon? polygon A 16.8 in. B 45 in. C 84 in. D 105 in. Big Polygon 2.5 Small Polygon 1 Write a ratio (scale factor) of the similar polygons x Big Polygon Small Polygon 42 Write a ratio of the perimeters of the similar polygons Define a variable of the unknown 3/3 Write a proportion of the 2 ratios x 2.5 = 42 1 Cross multiply 1x = 2.5(42) Bring down 1x = 1x = 105 x = 105 Multiply 2.5 42 A 16.8 in. Bring down = Use the Identify Property to multiply 1 x The variable is now by itself B 45 in. C 84 in. Answer: D 3/3 D 105 in. * MULTIPLE- CHOICE TEST ITEM A polygon has sides 3.5 times as long as a similar polygon. The larger polygon has a perimeter of 77 inches. What is the perimeter of the smaller polygon? A 22 in. B 34 in. C 72 in. Answer: A 3/3 D 269.5 in. Assignment Lesson 4:5 Similar Polygons 3 - 14 All