SIMILAR FIGURES ISOMETRIC corresponding sides congruent corresponding angles

SIMILAR FIGURES

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

To Find K (ratio of similarity) 5 initial 15 10 1 2 image 3 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: q q q q radius diameter circumference height width perimeter apothem ANY ONE DIMENSIONAL LENGTH

Ratio of Perimeter of Similar Figures 12 cm 6 cm 4 cm initial 8 cm 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

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

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