1. 4/24

2. Do Now 4/24 What is the solution to the equation -5 + √(x-9) = 4?
Essential Question: How can we determine the scale factor of dilation?

3. Agenda Do Now Good Things! Unit 4 Review
Notes: Congruence vs Similarity
ProblemAttic Partner Practice

4. Good Things!

5. Unit 4 Review Triangle Congruence Postulates
Transversal angle measures
Triangle Sum Theorem
Exterior Angle Theorem
Properties of Isosceles Triangles
Triangle Midsegment Theorem

6. Unit 4 Review Practice
Find m<B

7. Congruence vs Similarity
Congruent triangles have congruent angles and congruent side lengths
If we perform a rigid transformation on a triangle, we will always have two congruent triangles
What is the only non-rigid transformation we learned about?
Dilations!

8. Congruence vs Similarity
Are images that have undergone a dilation congruent to their preimage?? Unless the scale factor is 1…. NO! They are not congruent, they are similar Similar figures have the same shape, but are different in size

9. Congruent vs Similar

10. If we have a point (x,y) and a scale factor of k….
Similar Figures
The scale factor is what we multiply each coordinate by
Scale factor greater than 1  enlargement
Scale factor less than 1  reduction
Dilations preserve angle measure
If we have a point (x,y) and a scale factor of k….
Dk(x, y) = (kx, ky)

11. Scale Factor = Scale Factor Length of image side
Length of pre-image side
= Scale Factor
* You can also use this for coordinate points!
What is the scale factor of the
dilation (with center at the
origin) if point U (5, 7)
becomes U’ (25, 35)?

12. Scale Factor
The scale factor can be written in a variety of ways
Decimal
Fraction
Percentage
We always multiply the scale factor – regardless of how it is written!
Be careful when using calculator
Example: We have a triangle ABC. The length of AB is 7 units. After dilating the figure by 75%, what is the length of A’B’?

13. Distortions
Distortions happen when the width and height of a figure are not dilated at the same scale
If you can’t find a scale factor that works for the height AND the width, it’s a distortion!
Why would distortions be a bad thing?
Why are these bad?

14. Dilations – Finding the Scale Factor
Rectangle ABCD was transformed into rectangle EFGH through a dilation.
Enlargement or reduction? Why?
How can we determine the scale factor?
What is the scale factor of dilation?

15. Dilations - Vertices
As long as we know the coordinates OR the lengths of the sides, we can find the scale factor
A triangle has vertices G(2,–3), H(–6, 2), and J(0,4). If the triangle is dilated by a scale factor of 0.5 through center C (0, 0), what are the image vertices?
A triangle has vertices A(7,10), B(7,5), and C(-1, 5). If the triangle is dilated by a scale factor of 2.5 through the center C(0,0), what are the image vertices?
I can multiply each coordinate by the scale factor to find the new image vertices

16. Dilations – your turn!
Triangle MNO has the following vertices: M (-5, 8), N(7,-3), and O(-10,-4). After being dilated, triangle M’N’O’ now has the following vertices: M’(-3.75, 6), N’ (5.25, -2.25), and O’(-7.5, -3).
Is this an enlargement or reduction?
What is the scale factor of dilation?

17. Partner Practice
Must show work on a sheet of paper to receive credit for today’s work
When you are done, you may begin on this week’s independent practice