Warm-Up
BellExercises
Work
Are the polygons always, sometimes, or never similar?
1. Two isosceles triangles.
2. Two equilateral triangles.
3. A right triangle and an isosceles triangle.
4. A scalene triangle and an isosceles triangle.
Warm-Up
Exercises
Notes
Definition
Dilation
A transformation that preserves angle measures and results in
an image with lengths proportional to the preimage lengths.
If a dilation can be used to move one figure onto another, the
two figures are similar.
If a dilation followed by any combination of rigid motions can be
used to move one figure onto the other, the two figures are
similar.
Warm-Up
Exercises
Notes
Dilations
(x,y)
(kx, ky)
What is k?
Warm-Up
Exercises
Example
Dilations
(x,y)
(kx, ky)
Graph a triangle w/
one vertex at (0,0).
Graph a dilation of
the triangle w/ scale
factor 2 and centered at the origin.
EXAMPLE
Warm-Up2Exercises
Describe a combination of transformations
ABC is similar to FGE. Describe a combination
of transformations that moves ABC onto FGE.
Warm-Up
Exercises
GUIDED
PRACTICE
for Examples 1 and 2
The two figures are similar. Describe the
transformation(s) that move the blue figure onto the red
figure.
1.
2.
EXAMPLE
Warm-Up3Exercises
Use transformations to show figures are not similar
Use transformations to explain why ABCDE and KLQRP
are not similar.
EXAMPLE
Warm-Up3Exercises
Use transformations to show figures are not similar
SOLUTION
Corresponding sides in the pentagons 2
are proportional with a scale factor of 3 .
A dilation with center A and scale
factor 2 moves ABCDE onto
3
AFGHJ. Then a reflection moves
AFGHJ onto KLMNP.
Since angle measure is not preserved, the two pentagons
are not similar.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
Describe the dilation that moves the smaller figure onto
the larger figure.
1.
Daily
Homework
Warm-Up
Exercises
Quick
CheckQuiz
Describe the dilation that moves the smaller figure
onto the larger figure.
2.
Warm-Up
Exercises
For Tomorrow
Homework
HW: 6.2 Worksheet