I won't do any more "Day in the Life" posts for this subbing assignment, but there are a few things I want to say. Meanwhile, today is the second of four days of subbing in the digital film class. The area of ∆RST is 1 square inch.Lesson 12-9 of the U of Chicago text is called "The AA and SAS Similarity Theorems." In the modern Third Edition of the text, the AA and SAS Similarity Theorems appear in Lesson 12-7. The common ratio is called the scale factor.Ī ∆RST is dilated by a scale factor of 3 to form ∆R’S’T’. If two polygons are similar means they have the same shape, corresponding angles are congruent and the ratios of lengths of their corresponding sides are equal. To be proficient in math, you need to look closely to discern a pattern or structure. Compare the perimeters of ∆A’B’C and ∆ABC. Dilate ∆ABC to form a similar ∆A’B’C’ using any scale factor k and any center of dilation.Ī. Work with a partner: Use dynamic geometry Software to draw any ∆ABC. Do you obtain similar results?įrom the newly transformed triangles in part (a) and (b), side lengths of the triangles are changed by the scale factor of k and angle measures remain the same for both of the triangles ΔABC. Repeat parts (a) and (b) for several other triangles, scale factors, and centers of dilation. Plot these points on a coordinate plane to form a triangle ΔABC.Ĭ. Let the coordinates of the triangle to be A(2,2),B(1,3) and C(5,5). Find the ratios of the lengths of the sides of ∆A’B’C’ to the lengths of the corresponding sides of ∆ABC. Comparing the angle of ∆ABC and ∆A’B’C’ī. Comparing the side length of ∆ABC and ∆A’B’C’ģ. Comparing the coordinates of ∆ABC and ∆A’B’C’Ģ. Compare the corresponding angles of ∆A’B’C and ∆ABC.Ĭomparing the coordinates side lengths, and angle measures ∆A’B’C and ∆ABCġ. Dilate ∆ABC to form a similar ∆A’B’C’ using an scale factor k and an center of dilation.Ī. Work with a partner: Use dynamic geometry software to draw any ∆ABC. Volume of the rectangular prism V = 3 x 4 x 5 = 60 in³ The surface area of the rectangular prism A = 2(3 x 4 + 4 x 5 + 5 x 3) (c) Surface area is 1504 sq in, volume is 3840 cubic in (b) Surface area is 846 sq in, volume is 1620 cubic in (a) Surface area is 376 sq in, volume is 480 cubic in Find the surface area and volume of the image of the prism when it is dilated by a scale factor of Yes, the ratios \(\frac\) x 8 = 2Ī rectangular prism is 3 inches wide, 4 inches long, and 5 inches tall. Tell whether the ratios form a proportion. Similarity Maintaining Mathematical Proficiency
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