Name: Target 4 Perform compositions of figures to determine the coordinates and location of the image
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1 Unit 8 Similarity Figures and Dilations Target 1 Use proportions to identify lengths of corresponding parts in similar figures Target 2 Perform and identify dilations Target 3 Use ratios of lengths, perimeter, & area to determine unknown corresponding parts 3.3a Use Scale Factor & Similarity to Determine Unknown Lengths in Polygons & Circles 3.3b Use Scale Factor & Similarity to Determine Unknown Corresponding Parts Target 4 Perform compositions of figures to determine the coordinates and location of the image Name:
2 3.1 Similar Figures Target 1 Use proportions to identify lengths of corresponding parts in similar figures Vocabulary Similar Polygons: change of or of a figure) Linear Scale Factor: of the of sides. (location, size) (ratio, lengths, corresponding) Example 1: Use similarity statements In the diagram, ΔABC~ ΔDEF. 1. List all pairs of congruent angles! 2. Check that the ratios of corresponding side lengths are equal. Ratio 1: Ratio 2: Ratio 3: Are all three ratios equal? 3. Write the ratios of the corresponding side lengths in a statement of proportionality. Example 2: Find the linear scale factor Determine whether the polygons are similar. If they are, write the similarity statement and find the scale factor of ABCD to JKLM. Step 1: Identify pairs of congruent angles (Write congruent statements for all pairs) Step 2: Show that corresponding side lengths are proportional. Ratio 1: Ratio 2: Ratio 3: Ratio 4: Are all four ratios equal? Linear Scale Factor:
3 YOU TRY NOW! a) ΔABC~ΔDEF. What is the length of ED? b) The triangles are similar: ΔDEF~ΔRQP.Which angles are congruent? c) What is the length of FE? The triangles are similar.
4 3.2 Dilations Target 2 Perform and identify dilations Vocabulary Dilation: a transformation where the or of a figure occurs, where the sides are or proportionally about a center. Dilations do not change the of the. Example 1: Identify dilations Determine whether the dilation is a reduction (shrink) or an enlargement (expand). Find the scale factor of the dilation. a) (shrinking, expanding, shrink, expand, measures, angles) b) Example 2: Perform a dilation Dilate AB by a scale factor of!!. Example 3: Use scalar multiplication in a dilation The vertices of triangle ABC are A (-3, 0), B (0, 6), C (3, 6). Use scalar multiplication to find A B C after a dilation with is center at the origin and a scale factor of!. Graph ABC and its image.!
5 YOU TRY NOW! a) Calculate the scale factor for the dilation shown. b) ΔABC is dilated to form triangle ΔA! B! C. If!"!!!! = 7, what is!!!!!"? c) The vertices of ΔABC is A (-7, 8), B (7, -5), C (8, 10). Find the vertices of the dilated image with scale factor of!. The center of the dilation is the origin.! QUESTIONS OR REFLECTION What concepts were important to take away from this target? Questions? 1) Questions a) Summary 2) b) 3) c) 4) d)
6 3.3a Use Scale Factor & Similarity to Determine Unknown Lengths in Polygons & Circles Target 3 Use ratios of lengths, perimeter, & area to determine unknown corresponding parts Example 1: Use similar polygons to find lengths of unkown corresponding parts The two rectangular swimming pools are similar. How far is it diagonall across each pool? FUN FACT! All circles are similar! All angles are congruent because circles have a 360 angle. All lengths are proportional because radii and circumferences are proportional! Example 2: Use similar polygons to find lengths of unkown corresponding parts A high school wants to build a basketball court that is similar to an NBA basketball court, which is 94 feet long and 50 feet wide. Unforunately, the high school has room for a court that is 42 feet wide. How long should the court be, to the nearest foot? The scale factor is 7 5 or 5 7 QUESTIONS OR REFLECTION Write down at least 2 questions from this page to ask the next day. 1) 2)
7 YOU TRY NOW! a) The vertex of J of a regular hexagon has the coordinates (-6, 27). If the hexagon is dilated by a factor of!. Note: Regular means that all sides of! a polygon are the same length and all interior angles are congruent. b) Given the similar trapezoids ABCD and EFGH below, identify the side that is proportional to BC. c) The vertex of B of an octagon is located at (24, -16). The octagon is dilated by a factor of 0.25, with the center of dilation at the origin. What are the coordinates of B? d) Parallelograms ABCD and EFGH are similar. What is the length of GH? QUESTIONS OR REFLECTION Write down at most 2 questions that you can ask the next day. BE SPECIFIC. 1) 2)
8 3.3b Use Scale Factor & Similarity to Determine Unknown Corresponding Parts Target 3 Use ratios of lengths, perimeter, & area to determine unknown corresponding parts PERIMETERS OF SIMILAR POLYGONS If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. If KLMN ~ PQRS, then KL + LM + MN + NK PQ + QR + RS + SP = Example 1: Find the perimeter of similar figures A larger cement court is being poured for a basketball hoop in place of a smaller one. The court will be 20 feet wide and 25 feet long. The old court was similar in shape, but only 16 feet wide. Find the scale factor of the new court to the old court. Find the ratio of the perimeters of the new court to the old court. Areas of Similar Polygons If two polygons are similar with the lengths of corresponding sides in the ratio a: b, then the ratio of their areas is :. Scale Factor: Side Length of Polygon 1 Side Length of Polygon 2 = Ratio of Perimeters: Ratio of the Areas:
9 Example 2: Find the ares of similar figures What is the area of triangle XYZ? ΔFMN~ΔXYZ. YOU TRY NOW! a) ΔABC~ΔDEF. AB = 3 inches, DE = 6 inches, and the area of ΔABC is 72 square inches. What is the area of ΔDEF? b) ΔABC~ΔDEF. Both triangles are also isosceles triangles. AB = 5 inches, EF = 21 inches, and the altitude (height) of ΔABC = 4. The altitudes bisect (divides in half) the bottom sides of the triangles. Calculate the altitude of ΔDEF.
10 3.4 Similarity and Transformations Target 4 Perform compositions of figures to determine the coordinates and location of the image Example 1: Perform the composition The vertices of a triangle ABC is shown below. The triangle is translated 5 units to the right creating image A B C. Then, the image is reflected across the x-axis. Finally, the triangle is dilated by a factor of 1.5. What are the final coordinates of triangle A B C? ABC Coordinates after each transformation A B C A B C A B C A(, ) A (, ) A (, ) A (, ) B(, ) B (, ) B (, ) B (, ) C(, ) C (, ) C (, ) C (, ) SUMMARY In your own words, describe what a composition is.
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Date Target Assignment Done! W Review Worksheet. F 9-30 Project Cartoon Enlargement Project. T a 3.
Unit 3 Similar Figures and Dilations Target 1: Use proportions to identify lengths of corresponding parts in similar figures. Target 2: Perform and identify dilations. Target 3: Use sclae factor and similarity
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