3.1+Identifying+Similar+Figures

11-2-08 JO Big idea: Many things in our world are mathematically similar and we can use this to understand and describe the world around us. Essential question: How can I use math to check if two figures are similar? Class Notes:
 * Similar:** Figures with the same shape. Two figures are mathematically similar if their corresponding angles are equal and the ratios of all pairs of corresponding sides are equal


 * 3.1**

** Examine the four sets of polygons on labsheet 3.1. Two shapes in each set are similar, and the other is an impostor. ** **
 * In each set, which polygons are similar? Explain your answers. You may cut out the polygons if it helps you think about the question. **
 * Rectangle set ** : A and C are similar because C is a quadruple size of A (about). So if you change this to rules, A would be (x,y) and C would be (4x,4y).
 * Parallelogram set ** : B and C are similar because if you measure the length of each side, C is the double of B. So if B’s rule is (x,y), then C’s rule is (2x,2y).
 * Decagon set ** : A and C are similar because A and C have the same angle with each other. B doesn’t have the same angle with either A or C. If A’s rule was (x,y), then B’s rule might have been (x,2y). It got longer.
 * Star set ** : C and B are similar because they have the same length, same angles, and same general shape. A has the same angle as both of them too. But the perimeter of C and B is 13. 13 multiplied by 0.5= 6.5. Then the perimeter of A is 6. 6 and 6.5 aren’t the same numbers. So that means that A is different for both of them which makes B and C

3.1 F.U **** 1. for each pair of similar figures on labsheet 3.1, tell what number the side lengths of the small figure must be multiplied by to get the side lengths of the large figure. (You learned that this number is the scale factor from the small figure to the large figure.) ** There are lots of different ways to make the original figure enlarged. But you have to make sure you multiply both x and y with the same numbers. Some possibilities are, (2x,2y), (3x,3y), (4x,4y) ect. If you want to shrink the original figure, you can multiply the perimeter by multiplying it by decimals. Some possibilities are, 0.1, 0.2, 0.3, 0.4, 0.5 ect. The scale factors in parts 1 and 2 are related because they are both making shapes that are similar to the original shape they had but with different sizes. So you are seeing the original shape with different sizes but still will have the same angles, general shape, and either half shrunk or doubled side lengths and other numbers you multiplied with.
 * 2. For each pair of similar figures on labsheet 3.1, tell what number the side lengths of the large figure must be multiplied by to get the side lengths of the small figure. (This number is the scale factor from the large figure to the small figure.) **
 * 3. How are the scale factors in parts 1 and 2 related? **