SIMILAR FIGURES

ISOMETRIC VS SIMILAR -corresponding sides congruent -corresponding angles congruent -corresponding sides proportional -corresponding angles congruent These are IDENTICAL SHAPES moved by 4 isometries translation (t) rotation (r) reflection (s) glide reflection (gr) DILATATION - enlarge or reduce from initial (1st) to image (2nd). Think of a photocopy machine K is the symbol for ratio of similarity

To Find K (ratio of similarity) 5 10 15 initial 2 3 image 1 Ratio : measure of image measure of initial Ratio: 1 or 2 or 3 5 10 15 Ratio: is K= 0.2 To find the ratio of similarity, use corresponding side lengths.

Side lengths could be: radius diameter circumference height width perimeter apothem ANY ONE DIMENSIONAL LENGTH

Ratio of Perimeter of Similar Figures 6 cm 4 cm 12 cm 8 cm initial image Perimeter=20 Ratio of sides = 12 = 2 (this is the ratio of corresponding sides) 6 K = 2 Ratio of perimeters: K = 2 To find perimeter of image: Perimeter of initial x K = perimeter of image 20 x 2 = 40

Find the perimeter of the image of these 24 cm Find the perimeter of the image of these similar right triangles. 10 cm 6 cm initial Step 1- Find missing side on initial triangle. (use Pythagoras or remember the triples) Missing side = 8 cm Step 2 – Find K 24 = 3 K = 3 8 Step 4- Calculate the perimeter of the image P initial X K = P initial 24 X 3 = 72 Step 3- Calculate the perimeter of the initial P = 8 + 6 + 10 P = 24

Finding the Area of Similar Solids Area of initial X K2 = Area of image 6 image 5 2 initial Step 1 – Find K 6 = 3 2 Step 2 – Find area of image (2 x 5) X 22 = 40 cm2