1. Similar Figures (Not exactly the same, but pretty close!)

2. Let’s do a little review work before discussing similar figures.

3. Congruent Figures In order to be congruent, two figures must be the same size and same shape.

4. Similar Figures Similar figures must be the same shape, but their sizes may be different.

5. Similar Figures This is the symbol that means “similar.” These figures are the same shape but different sizes.

6. SIZES Although the size of the two shapes can be different, the sizes of the two shapes must differ by a factor. 33 2 1 6 6 2 4

7. SIZES In this case, the factor is x 2. 33 2 1 6 6 2 4

8. SIZES Or you can think of the factor as 2. 33 2 1 6 6 2 4

9. Enlargements When you have a photograph enlarged, you make a similar photograph. X 3

10. Reductions A photograph can also be shrunk to produce a slide. 4

11. Determine the length of the unknown side. 12 9 15 4 3 ?

12. These triangles differ by a factor of 3. 12 9 15 4 3 ? 15 3= 5

13. Sometimes the factor between 2 figures is not obvious and some calculations are necessary. 18 12 15 12 108 ? =

14. To find this missing factor, divide 18 by 12. 18 12 15 12 108 ? =

15. 18 divided by 12 = 1.5

16. The value of the missing factor is 1.5. 18 12 15 12 108 1.5 =

17. Solving for the Missing Side Using Proportions One more way to solve proportions: 2 = 6 2 x n = 6 x 8 2n = 48 8 n 2 2 n = 24 8 n 6 2

18. When changing the size of a figure, will the angles of the figure also change? ?? ? 70 40

19. Nope! Remember, the sum of all 3 angles in a triangle MUST add to 180 degrees. If the size of the angles were increased, the sum would exceed 180 degrees. 70 40 70 40

20. 70 40 We can verify this fact by placing the smaller triangle inside the larger triangle. 70 40

21. 70 40 The 40 degree angles are congruent.

22. 70 40 The 70 degree angles are congruent.

23. 70 40 4 The other 70 degree angles are congruent.

25. Step 1 Draw a right triangle. B C A Label each angle. Cut out the triangle.

26. Step 2 Cut off the angles as shown. B AC

27. Step 3 Place the angles together at a point to form a straight line. A B C

28. A B C The angles placed together form a straight line. A straight line or straight angle is equal to 180º. Therefore, the sum of all the angles in a triangle is equal to 180!º

29. You can use this fact to find the missing angle in a triangle. For example, lets say I have the following triangle: 80º45º ? I know the measurements of two of the angles, but the third one is a mystery. How do I find the measurement of that third angle?

30. Remember that all the angles in a triangle added together equal 180.º So: 80º + 45º + ? º = 180º It’s an equation! 125º + ?º = 180º Step 1: Add 80º + 45º Step 2: Subtract 125º from both sides ?º = 55º Answer! 80º45º ? Check: 80º + 45º + 55º = 180º √

31. Lets try another: 32º 24º ?º 32º + 24º + ?º = 180º Step 1: Add 32º + 24º 56º + ?º = 180º Step 2: Subtract 56º from both sides ?º = 124º Answer! Check: 32º + 24º + 124º = 180º √

32. This one is a bit tricky...but I think you can do it!!! 45º ?º Hmmm....this one has a 45º angle, a mystery angle, and an angle with a square corner. When you remember what that square corner means, put your finger by your nose. (Remember: no nose picking allowed!) Yes! The square corner means that it is a right angle. I know that a right angle is equal to 90.º

33. 45º ?º So... 45º + 90º + ?º = 180º Step 1: Add 45º + 90º 135º + ?º = 180º Step 2: Subtract 135º from both sides ?º = 45º Answer! Check: 45 + 90º + 45º = 180º √

34. THE END!