What You ll Learn. Name: Date: CHAPTER 9 NOTES Scale Diagrams & Similarity Calendar of Chapter: See the Homework link on the webpage
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1 Name: Date: CHAPTER 9 NOTES Scale Diagrams & Similarity Calendar of Chapter: See the Homework link on the webpage What You ll Learn 9.1 draw and interpret enlargement scale diagrams 9.1 draw and interpret reduction scale diagrams 9.2/9.3 learn and apply properties of similar shapes What are some careers that require either the construction or analysis of scale diagrams? Here is some useful information for Similarity (Ch 9): - If the sides of a shape have the same dash mark(s), they re equal in length - An isosceles triangle has two equal sides and two equal angles - Sides are described with two capital letters ex. AB - Angles are described with three capital letters ex. <ABC - If you know two sides of a right triangle, you can find the 3 rd side using Pythagoras - The three angles in a triangle always add to 180 degrees
2 9.1A Scaling: Enlargements Focus: Draw and interpret scale diagrams that represent enlargements. Warmup: Shape A is the original. Shapes B, C, D, & E are all possible enlargements. a) Which one(s) are enlargements of A? b) How can you be certain? c) Show, using numbers, that your choices are correct. What does proportional mean? What is a scale diagram? What are corresponding lengths? What is a scale factor? What are the two ways to write a scale factor? What is an enlargement, and how can you tell an enlargement by the scale factor? When are scale diagram enlargements used in society?
3 Ex1 Look at the Act 1 picture of Gulliver s Desk. a) What questions come to mind? b) What information do we need? c) Find the scale factor compared to human (original) size. d) Find the height of the chair if it is human (original) size. Ex2 - A scale factor for a filing cabinet is 3 8. a) Is it an enlargement or a reduction? b) If the scale diagram has a length that is 60cm, what is the actual length of the original? Ex3 - A scale factor for a computer chip is is 9:1 (same as 1 9 ). If the length of the original chip is 6mm, what is the length on the scale model? Ex4 - Draw a scale diagram of the drawing. Use a scale factor of 1.5.
4 9.1B Scaling: Reductions (DISCOVERY LESSON) Focus: Draw and interpret scale diagrams that represent reductions. Warmup: Find the scale factor of the enlargement: *Use the same units For all measurements! Original Scale Drawing How are all scale factors written (review of last class)? What is a reduction, & how can you tell a reduction by the scale factor? When are scale diagram reductions used in society? Ex1 Use a ruler to determine the scale factor in decimal form. Scale Drawing Scale Drawing Original
5 Ex2 A scale factor for a reduction of a chair is 1: 8 (same as 8 1 ). If the height of the actual chair is 75cm, what is the height on the scale drawing? Ex3 As a class, watch Act 1 of Splittime. a) What questions come to mind? b) What do we need to know? c) Do the math! d) Watch Act 3 to get the answer. e) How many laps of the indoor track equal one lap of the outdoor track?
6 9.2/9.3 Similar Triangles (and Other Polygons) Focus: Recognize, draw, & solve problems for similar triangles (and other polygons). Warmup: What is alike about the two triangles, and what is different? What does similar mean in geometry? What are similar triangles? Using the similar triangles from the warmup, describe the relationships between the angles, and the relationships between the sides. Ex1 a) The triangles are similar. Write a statement to represent this. b) Solve for sides XZ & side ZY.
7 Ex2 How can we find the height of the lamppost without measuring it directly? Answer to the nearest tenth. Ex3 The two triangles are similar. Find the missing lengths. A 6.2m 11.4m B 9.6m C D 4m E What is a polygon? Similar polygons have the same characteristics as similar triangles. Ex4 The polygons are similar. Find B sides x and y. 40cm C B A 20cm C 30cm Keep the scale factor A as a fraction and use 50cm D x cross-multiply. y E 80cm D E 45cm
8 Ex5 Which, if any, rectangles are similar? Use a ruler and make fractions to confirm. A B C
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