1. Chapter 7
Isometry & similitude

2. 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'

3. 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'

4. 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)

5. SIMILAR FIGURES

6. 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
Ratio is k=0.2
Image
Initial 10 3 5 15

7. 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

8. 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

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

10. Example Step 1 - Find the missing side of initial triangle
(use Pythagoras)
missing side: 8cm
Step 2 – Calculate perimeter
of the initial
p =
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

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