dilations per 3.notebook October 28, 2015 Module 3 Similarity Dilations

Transcription

1 Module 3 Similarity Dilations 1

2 Which of these figures are dilations? What do you think is the definition of a dilation? reduction enlargement scale factor point of dilation 2

3 Dilations on a Coordinate Plane Which triangle is the original figure and which one is the dilation? How do you know? What are the coordinates of the: triangle triangle A B C A' B' C' What is the scale factor? A 8 6 A' 4 B C B' C' What are the coordinates of the: pink triangle A B C blue triangle A' B' C' What is the scale factor? 3

4 H ( 1,3) J (3,2) K (2, 3) L ( 2, 2) Scale Factor of 2 Let's Practice A ( 6,2) B (4,4) C (7, 2) D ( 2, 4) Scale Factor of 1/4 After you determine the new prime points, plot the points on a coordinate plane for the original figure and the dilated figure to see if the figures look correct. Identify the center of dilation. LINE SEGMENTS 4

5 Segment P'Q' is a dilation of segment PQ. Find the scale factor of the dilation if the points are P( 3, 3) and Q(3,0) and P'( 2, 2) and Q'(2,0). Complete the Exit Ticket and it hand in. 1. Find the coordinates of the vertices of the figure A'B'C'D' after it has been dilated with the scale factor of 4. A( 8,4) A'( ) B(6,4) B'( ) C(6, 4) C'( ) 2. Find the scale factor of line segment AB (6,3) (6,9) and its dilation line segment A'B' (2,1) (2,3). Scale Factor= 5

6 Dilations copied page Assignment: More Dilations 6

7 The vertices of a trapezoid are A ( 2, 1), B( 1,1), C(0,1), and D(0, 1). Dilate the trapezoid with respect to the origin using a scale factor of 2. Then translate it 6 units right and 2 up. What are the coordinates of the transformed image A'B'C'D'? The red figure is similar to the blue figure. Describe the sequence of transformations in which the blue figure is the image of the red figure. 7

8 Complete the Exit Ticket and raise your hand when you finish. B Triangle A is similar to the triangle B. Describe the sequence of transformations in which triangle B is the image of triangle A. A BI 2.7 #1 27 odd Assignment: 8

9 ENY Lesson 2 Properties of Dilations (you need a ruler and protractor) Take out pages S7 9 9

10 Complete the Exit Ticket independently and raise your hand when you've completed it. Assignment: ENY 3.2 PS #1 3 ENY Lesson 6 Dilations on a Coordinate Plane/Graph 10

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12 How can we find the coordinates for the vertices of a figure that is dilated if we are given the original coodinates and the scale factor? W = (2, 3) W' = X = (3, 4) X' = Y = ( 2, 7) Y' = Z = ( 5, 4) Z' = scale factor: 5 A = ( 6, 2) A' = B = ( 1, 3) B' = C = (4, 5) C' = scale factor: 2 3 Take out S

13 Complete the Exit Ticket independently and raise your hand when you've completed it. Assignment: ENY 3.6 PS #1 5 ENY Lesson 3 Examples of Dilations 13

14 Take out S13 14 Complete the Exit Ticket independently and raise your hand when you've completed it. Assignment: ENY 3.3 PS #1 5 14

15 ENY Lesson 4 Fundamental Theorem of Similarity (FTS).. O P OP OP OP OP 15

16 dilations per 3.notebook Fundamental Theorem of Similarity scale factor= If there is a center of dilation and there are two rays with 2 points with the same scale factor then two parallel lines are created when connecting the points r PQ = P'Q' Take out S17, L4 Problem Set, and the Exit Ticket Complete S17 with a partner 16

17 Complete the Exit Ticket independently and raise your hand when you've completed it. Assignment: ENY 3.4 PS #1 4 ENY Lesson 5 Converse of FTS Fundamental Theorem of Similarity 17

18 What is the First Fundamental Theorem of Similarity? hypothesis conclusion hypothesis conclusion The converse is starting with the conclusion and coming up with the hypothesis. Examples of converses of a sentence: hypothesis If I have an umbrella, then it's raining outside. conclusion If it's raining outside, I probably have an umbrella. hypothesis conclusion hypothesis conclusion If we turn on the faucet, then water comes out. If Take out all the pages for Lesson 5. 18

19 Complete the Exit Ticket independently and raise your hand when you've completed it. Assignment: ENY 3.5 PS #1 3 19