CCSS Content Standards G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 6 Attend to precision. 4 Model with mathematics.
Then/Now You identified congruence transformations. Identify similarity transformations. Verify similarity after a similarity transformation.
Example 3 Verify Similarity after a Dilation A. Graph the original figure and its dilated image. Then verify that the dilation is a similarity transformation. original: M(–6, –3), N(6, –3), O(–6, 6) image: D(–2, –1), F(2, –1), G(–2, 2) Graph each figure. Since M and D are both right angles, M D. Show that the lengths of the sides that include M and D are proportional.
Example 3 Verify Similarity after a Dilation Use the coordinate grid to find the lengths of the vertical segments MO and DG and the horizontal segments MN and DF. Answer:Since the lengths of the sides that include M and D are proportional, ΔMNO ~ ΔDFG by SAS Similarity.
Example 2 Find and Use a Scale Factor PHOTOCOPYING A photocopy of a receipt is 1.5 inches wide and 4 inches long. By what percent should the receipt be enlarged so that its image is 2 times the original? What will be the dimensions of the enlarged image? To enlarge the receipt 2 times the original, use a scale factor of 2. Written as a percent, the scale factor is (2 ● 100%) or 200%. Now, find the dimensions of the enlarged receipt. width: 1.5 in. ● 200% = 3 in. length: 4 in. ● 200% = 8 in. Answer: The enlarged receipt will be 3 inches by 8 inches.
Example 2 Identify Similar Polygons MENUS Tan is designing a smaller menu for the restaurant where he works to conserve paper. Determine which menu option retains similar measures to the original. Explain your reasoning. Original Menu: Option A:Option B:
Assignment: – Multiple Choice Practice – Homework Quiz Wednesday – Test Chapter 7 Friday Geometry Even if you're on the right track, you'll get run over if you just sit there. Will Rogers