Grade 9 Math. Unit 7a: Similarity. May 14 9:04 AM. Types of Triangles and Their Properties. Identifying triangles based on side length:
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1 Grade 9 Math Unit 7a: Similarity May 14 9:04 AM Types of Triangles and Their Properties Identifying triangles based on side length: Identifying triangles based on angle size: May 14 9:05 AM 1
2 Interior Angles of a Triangle The interior angles of a triangle add up to. ex. Find the missing angle measure: A A B C B C May 14 9:10 AM ex. Find the missing angle measure: A A B C B C May 14 9:14 AM 2
3 7.1 Scale Diagrams and Enlargements Scale Factor is a fraction that compares the original shape's size to an enlargement/reduction of that same shape. Represented by a fraction: Scale Factor = Side length of scale diagram Side length of original diagram A Scale Diagram is an enlargement or reduction of another diagram. May 14 10:43 AM ex. Find the scale factor of this diagram: Original length of mosquito is 12 mm. Image of the mosquito in an article is 4.5 cm. May 14 10:49 AM 3
4 We can use scale factor to find the length of a scale object from an original object. ex. If a mosquito measures 12 mm. How large would a diagram be that uses a scale factor of 3? May 19 9:59 AM May 19 10:09 AM 4
5 ex. A photo has the dimensions 9 cm by 6 cm. If the photo is enlarged by a scale factor of What are the new dimensions? May 19 10:11 AM Draw a scale diagram of this metal bracket. Use a scale factor of cm 3 cm 2 cm 3 cm 1 cm May 19 10:50 AM 5
6 Draw a scale diagram of this metal bracket. Use a scale factor of cm 0.5 cm 0.5 cm 1.5 cm May 19 10:50 AM May 26 9:55 AM 6
7 May 26 10:31 AM May 26 10:36 AM 7
8 May 26 10:43 AM May 26 10:48 AM 8
9 May 26 11:07 AM May 29 10:04 AM 9
10 May 26 11:10 AM May 29 10:33 AM 10
11 7.2 Scale Diagrams and Reductions When the scale factor is greater than 1, it is an enlargement. When the scale factor is between 0 and 1, it is a reduction. ex. If a Boeing 747 airplane is m and the model is 15 cm, what is the scale factor? Use the same formula as before! May 20 10:27 AM May 30 9:56 AM 11
12 ex. Which of these shapes are a reduction of the original? We need to check if all sides have the SAME scale factor. May 21 10:27 AM ex. Reduce this diagram by a scale factor of May 22 9:57 AM 12
13 7.3 Similar Polygons When we enlarge or reduce a diagram, we say that the new diagram is similar to the original diagram. Important terms Corresponding Sides: Matching sides (same position) Corresponding Angles: Matching angles (same position) May 26 9:47 AM ex. Identify pairs of similar rectangles. Justify your answer. 1: Check angles - need to all be equal 2: Check side lengths - need to be in proportion May 26 10:15 AM 13
14 May 31 10:15 AM You can use similarity to find missing measurements of a shape: ex. Find the measure of the missing side. These shapes are similar: G L A F B C D E H I J K May 28 9:56 AM 14
15 ex. If you have a toy plane that is 21.5 cm long and has a wing span of 18 cm, and it is similar to a real plane that is 63 m long, what is the real plane's wing span? May 28 10:32 AM Jun 2 9:56 AM 15
16 Jun 2 10:14 AM 7.4 Similar Triangles ex. Identify the similar triangles: Jun 2 10:22 AM 16
17 4. Jun 5 9:58 AM Finding missing sides using Similar Triangles: You can use proportional reasoning to find the info Cross multiplying is useful!!! ex. Ryland is 1.8 m tall. His shadow at a certain time of day is 1.3 m long. At the same time, the shadow of a totem pole is 6 m long. How tall is the totem pole to the nearest tenth? Jun 2 10:53 AM 17
18 ex. Skie and Natalie are surveyors. They want to measure across a lake, which is impossible. They measure the distance and angles on land, and then sketch this diagram. How long is the lake? Jun 3 10:31 AM Jun 5 10:36 AM 18
19 Jun 6 10:19 AM Review 1) Find scale factor: Jun 8 10:06 AM 19
20 2) Use scale factor to find a missing length: Jun 8 10:13 AM 2) Use scale factor to find a missing length: Jun 8 10:18 AM 20
21 3) Cross multiplication: Jun 8 10:25 AM 4) Proving similarity: - Between 2 or more objects! Looking for: 1. All corresponding angles the same 2. All corresponding sides in proportion (same scale factor) Jun 8 10:32 AM 21
22 5) More complicated questions Jun 8 10:39 AM Demonstrate understanding of similarity of 2 D shapes. a. Observe and describe 2 D shapes, relevant to self, family, or community, that are similar. b. Explain the difference between similarity and congruence of polygons. c. Verify whether or not two polygons are similar. d. Explain how ratios and proportionality are related to similarity of polygons. f. Solve situational questions involving the similarity of polygons. e. Draw a polygon similar to a given polygon and explain the strategies used. g. Identify and describe situations relevant to self, family, or community that involve scale diagrams and explain the meaning of the scale factor involved. h. Explain how scale diagrams are related to similarity, ratios, and proportionality. i. Draw a diagram to scale that represents an enlargement or reduction of a given 2 D shape and explain the strategies used. j. Explain how to determine the scale factor for a given 2 D shape and an enlargement or reduction of the shape. k. Verify whether or not a given diagram is a scale diagram of a 2 D shape and, if it is, identify the scale factor for the diagram. l. Solve situational questions involving scale diagrams and scale factors. Jun 2 10:25 AM 22
23 I can show that I understand similarity of 2D shapes: I can find scale factor, given two similar shapes. I can find the side length of a scale diagram, given the original shape and the scale factor. I can find the side length of the original shape, given the scale diagram and the scale factor. I can draw an enlargement or a reduction, given a shape and a scale factor. I can prove similarity between two shapes (or disprove). I can use cross-multiplication to find missing side lengths, given two similar shapes. Jun 7 10:22 AM 23
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