1. 4.1: Dilations and Similar Triangles Tonight’s Homework: 4.1 Handout
WELCOME
Chapter 4: Similarity
4.1: Dilations and Similar Triangles
Tonight’s Homework: 4.1 Handout

2. Warm Up
Solve the proportions: 1. 2.

3. Chapter 4 Learning Targets

4. Ratios a b = a : b Ratio of a to b = *Simplify when possible*
Relationship between two quantities using the same units.
*Simplify when possible* a b
= a : b
Ratio of a to b =

5. The ratio of the lengths for two corresponding sides
Scale Factor
The ratio of the lengths for two corresponding sides
ABCD ∼ EFGH E
10in F A
5in B
16in
8in D C H G

6. Congruence Vs. SimilarityD ≅ A F E C B

7. Dilation Investigation

8. (0,0)

10. Transformation Basics
Figures in a plane can be reflected, rotated, or translated to produce new figures.
Pre-image:
The original figure
Image:
The new version of the figure after being transformed
Transformation:
The operation that maps, or moves, the pre-image onto the image

11. Congruence Vs. Similarity≅ X D ∼ A M F E C B Z S P Y

12. A non rigid transformation where the image and preimage are similar
Dilation
A non rigid transformation where the image and preimage are similar F k p F C
The image is a dilation of the preimage with scale factor k:p from the center C

13. Reduction vs. Enlargement
0 < k < 1
Enlargement:
k > 1

14. Requirements For Dilation
Dilation with center C and scale factor K maps point P to P’, and…
If P is not on C, then P’ is on
CP. Also Scale factor k =
(k>0 and k≠1 )
2. If P is on C, then P=P’
CP’ CP P’ C P P
= P’ C

15. The ratio of the lengths for two corresponding sides
Scale Factor
The ratio of the lengths for two corresponding sides
ABCD ∼ EFGH E
10in F A
5in B
16in
8in D C H G

16. “ABCD is Similar to EFGH”
Similar Polygons
Polygons with all corresponding angles ≌ and all sets of sides proportional B
If ∠A ≌ ∠E & ∠B ≌ ∠F
∠C ≌ ∠G & ∠D ≌ ∠H
Then
“ABCD is Similar to EFGH” F A E H G D C
ABCD ∼ EFGH

17. Similar Polygons
Polygons with all corresponding angles ≌ and all sets of sides proportional A
If ∠A ≌ ∠E & ∠B ≌ ∠F
∠C ≌ ∠G
Scale Factor =
Then
“ABC is Similar to EFG” E G F C B
ABC ∼ EFG

18. Dilation on Coordinate Plane
When Dilating on the plane w/ (0,0) Multiply both the x and y value by the scale factor
(x,y) ->
(kx,ky)

19. Equations that equate two ratios are called proportions.b c d =

22. Proportion Practice

27. = = a x x d x a∙b Geometric Mean
Given two numbers ‘a’ & ‘d’ the geometric mean is the value ‘x’ such that…
and a x x d x
a∙b = =