1 Geometry Section 7-1A Changing the Size of Figures Page 462 You will need a calculator with sin/cos/tan in 2 weeks. Freshmen - TI 30 XII S recommended. Around $15. You’ll need it for Alg. II.

2

3 Similar Figures: Similar Figures- Figures that have the same shape, but not necessarily the same size. Think enlargements or reductions. These figures are similar. Same shape, but not the same size. These are not similar. None of these have the same shape. Pg. 462

4 Similar Figures: Scale Factor: the amount of enlargement or reduction needed to get one figure from another. If the scale factor is greater than 1, the similar figure is an enlargement; if the scale factor is less than 1, it is a reduction. Pg. 462

5 Explore: Enlarge the side lengths by a factor of 3. Pg. 463 Choose a side in the original figure. Identify the corresponding side in your enlarged version. What is the ratio between the 2 sides? Is it the same for other sets of corresponding sides? Use your protractor to measure the corresponding sets of angles. What is their ratio?

6 Explore: Enlarge the side lengths by a factor of 3. Pg. 463 Choose a side in the original figure. Identify the corresponding side in your enlarged version. What is the ratio between the 2 sides? Is it the same for other sets of corresponding sides? Use your protractor to measure the corresponding sets of angles. What is their ratio? The ratio of the lengths of two corresponding sides of similar figures is the similarity ratio.

7 Example:  ABC is similar to  XYZ. Pg. 463 AB 5 XY 9 Find the similarity ratio of  ABC to  XYZ. = Find the similarity ratio of  XYZ to  ABC. XY 9 AB 5 = z

8 Try It: a. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the figure on the left to the figure on the right. Pg. 464 If similar, find the similarity ratio of the figure on the right to the figure on the left. Similar 2/1 1/2

9 Try It: b. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the figure on the left to the figure on the right. Pg. 464 If similar, find the similarity ratio of the figure on the right to the figure on the left. Similar 1/3 3/1

10 Try It: c. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the figure on the left to the figure on the right. Pg. 464 Not similar

11 Try It: d. State whether or not this pair of figures is similar. For each pair of similar figures, find the similarity ratio of the figure on the left to the figure on the right. Pg. 464 If similar, find the similarity ratio of the figure on the right to the figure on the left. Similar; 1/3 3/1

12 Definition: Definition of similar: Two polygons are similar if and only if: 1)Their corresponding angles are congruent and 2)Their corresponding side lengths are proportional. Pg. 464

13 Reflect: Suppose you enlarge or reduce a figure to make a similar figure. Pg. 465 What happens to the measure of each of the angles? The angle measures stay the same. What happens to the length of each line segment? Side lengths are multiplied by the scale factor. If Figure X is similar to Figure Y, how is the similarity ratio from X to Y related to the similarity ratio from Y to X? They are reciprocals of each other.

14 Exercises: #4 Pg. 465 If you reduce a 15cm x 20cm rectangle by using a scale factor of 3/5, what will the dimensions of the reduced rectangle be? x = x =12 9cm x 12cm

15 Exercises: #5 Pg. 465 If you enlarge a 9 in x 12 in rectangle by using a scale factor of 2.5, what will the new dimensions be? 9 x 2.5 = x 2.5 = in x 30 in

16 Exercises: #6, 7 Pg. 466 True or False? Any 2 squares are similar. True Any 2 rectangles are similar. False. The ratio of the lengths could be different from the ratio of the widths.

17 Exercises: #8, 9 Pg. 466 True or False? Any 2 rhombuses are similar. False. The sides remain in proportion, but the angles can be changed. Any 2 equilateral triangles are similar. True. All angles will be 60 o and all sides will be proportional.

18 Exercises: #12 Pg. 466 A to B = 1/3 Each pair of figures is similar, and the length of corresponding sides are shown. Find the similarity ratio of Figure A to B and of B to A. B to A = 3/1

19 Exercises: #14 Pg. 466 Not similar. State whether or not each pair of figures is similar. If similar, find the similarity ratio of the figure on the left to the figure on the right. If not similar, explain why. Sets of corresponding sides do not have the same ratio.

20 Exercises: #15 Pg State whether or not each pair of figures is similar. If similar, find the similarity ratio of the figure on the left to the figure on the right. If not similar, explain why. Similar

21 Draw a similar figure using a scale factor of 3. #2 Pg. 465

22 Draw a similar figure using a scale factor of 1/2. #3 Pg. 465

23 Homework: Practice 7-1A Quiz Friday