Chapter 7. Isometry & similitude. Definitions. 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 Δ ABC = Δ A ' B ' C '. Definitions.
Chapter 7 Isometry & similitude
Definitions Two figures or solids areISOMETRIC(or congruent) if: 1. The correspondingsidesare congruent 2. The corresponding angles are congruent A A' C C' B B' ~ We write ΔABC = Δ A'B'C'
Definitions Two figures or solids areSIMILAR if: 1. The correspondingsidesare proportional 2. The corresponding angles are congruent A' A C C' B B' We write ΔABC ~ ΔA'B'C'
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 Geometric Transformations *** dilation + any isometry = composition (which is a similitude)
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
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 perimeters: k = 40 20 k = 2 Ratio of sides: k = 12 6 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
Workbook p. 216 (all) p. 217 Activity 3 p.221 #1,2,3 Homework – Start NOW