Chapter 7 Isometry & similitude

Definitions We write ΔABC = Δ A'B'C' ~ Two figures or solids are ISOMETRIC (or congruent) if: 1. The corresponding sides are congruent 2. The corresponding angles are congruent A A' C C' B B' ~ We write ΔABC = Δ A'B'C'

Definitions We write ΔABC ~ ΔA'B'C' Two figures or solids are SIMILAR if: 1. The corresponding sides are proportional 2. The corresponding angles are congruent A' A C C' B B' We write ΔABC ~ ΔA'B'C'

Geometric Transformations ISOMETRY SIMILITUDE Transforms a figure into an isometric figure Translation (t) Rotation (r) Reflection (s) Glide reflection (gr) Transforms a figure into a similar figure Dilation: Enlarge or reduce from the initial (1st) to the image (2nd) *think of a photo copy machine *** dilation + any isometry = composition (which is a similitude)

SIMILAR FIGURES

What is the ratio of similarity? k is the symbol for the ratio of similarity between two similar figures. HOW DO WE FIND ‘k’? 2 1 Ratio: measure of image measure of initial Ratio: 1 or 2 or 3 5 10 15 Ratio is k=0.2 Image Initial 10 3 5 15

ANY ONE Dimensional Length IMPORTANT!!!! To find the ratio of similarity, use CORRESPONDING side lengths. Side Lengths could be: Radius - Width Diameter - Perimeter Circumference - Apothem Height ANY ONE Dimensional Length

Ratio of Perimeter of similar figures 12cm 6cm Image Initial 8cm 4cm Perimeter: 20cm Perimeter: 40cm Ratio of sides: k = 12 6 k = 2 Ratio of perimeters: k = 40 20 k = 2

To find the perimeter of the image Scale factor: k perimeter of initial X k = perimeter of the image

Example Step 1 - Find the missing side of initial triangle (use Pythagoras) missing side: 8cm Step 2 – Calculate perimeter of the initial p = 8+6+10 p=24 Step 3 – Find k k = 24 = 3 8 Step 4 – Calculate the perimeter of the image P=24 x 3 = 72cm Find the perimeter of the image Initial 10 cm Image 6 cm 24 cm

Homework – Start NOW Workbook p. 216 (all) p. 217 Activity 3