Question

erimete 839 Math Activity 12.3 MATH ACTIVITY 12.3 Enlargements with Pattern Blocks Materials: Pattern Blocks in the Manipulative Kit or Virtual Manipulatives Virtual Manipulatives Purpose: Construct similar patten block figures and explore the effects of scaling. 1. The single trapezoid (red) at the left below is similar to the large trapezoid below it, which is formed with six pattern blocks. a. One condition for similarity is that ratios of the lengths of corresponding sides of two figures are equal. What is the ratio of the lengths of the corresponding sides of these two figures? b. The second condition for similarity is that the corresponding angles of the two figures have the same measure. Explain which angles in the two trapezoids are corresponding and how you know they have the same measure. c. Because each side of the large trapezoid is 2 times the length of each correspond- ing side of the small trapezoid, the large trapezoid is an enlargement of the small trapezoid by a scale factor of 2. The area of the large trapezoid is how many times the area of the small trapezoid? Write a sentence or two to explain your reasonin d. Construct an enlargement by a scale factor of 2 for each of the other five pattern blocks. Sketch figures and describe how the area of a figure is related to the area Enlargement by scale factor 2 of its enlargement *2. The large triangle at the left is an enlargement of the small triangle by a scale fac- tor of 3. Build and sketch an enlargement by a scale factor of 3 for each of the other five pattern blocks. (Trace pattern blocks, if there are not enough.) Explain how the area of each enlargement compares to the area of the single pattern block. h an enlargement of each of the following figures for the given 3. Build and sketc Enlargement by scale facior 3 scale factor b. Enlarge by a scale factor of 4 a. Enlarge by a scale factor of 3 d. Enlarge by a seale factor of 2 c. Enlarge by a scale factor of 3 e. State a conjecture about how you think the area of an enlargement is related to the area of the smaller figure. Write an explanation to support your reasoning

Answer 1

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and Area a Tata Zeidal Bas 2h 22b 2

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