1. Unit 7 – Similarity and Transformations
Section 7.3
Curriculum Outcome: Demonstrate an understanding of similar polygons

2. Corresponding Sides
If we enlarge/reduce an object, could we forget one side?
What would that look like if we did?
Why would we enlarge only three sides and forget the top side, or any other side either.

3. Corresponding Sides
If we enlarge/reduce an object, could we change the scale factor for all of the sides?
What would that look like if we did?
Is it even worth figuring out if this is an enlargement or a reduction?

4. Corresponding Sides
If we were trying to figure out the scale factor of an enlargement/reduction, can we mix and match our sides?
What would that look like if we did?
Could we match up the 4 with the 6 and the 3 with the 10?
If we did that, could we even figure out a scale factor between these two shapes? 5 4 10 3 8 6

5. Corresponding Sides So what do we need to do?
We need to work with ‘corresponding sides’.
We can see the scale factor between these two shapes is 2.
We would match the 4 with the 8, the 3 with the 6, and the 5 with the 10. 5 4 10 3 8 6

6. Proportional Corresponding Sides
When pairs of corresponding sides have lengths that are in the same ratio, the side lengths and ultimately the shapes are said to be proportional.
Each pair of sides has a ratio (scale factor) of 2.
That means that the sides are proportional and so are the shapes. 5 4 10 3 8 6

7. Proportional Corresponding Sides
For the two shapes below, we can recognize the corresponding sides and how each pair of sides are proportional , but what else would be similar?...Or even the same? 5 4 10 3 8 6

8. Corresponding Sides with Corresponding Angles
If these triangles are similar, shouldn’t the angles be similar too?
In fact in order for these two triangles to be similar, the corresponding angles must be similar too. * 5 * 4
< 10 3 8
< 6

9. Properties of Similar Polygons*
Their corresponding angles are equal.
Their corresponding sides are proportional.
*Polygons = Shapes * 5 * 4
< 10 3 8
< 6

10. Prove it, Tough Guy! A * 2 3 B ^
So let’s start to match corresponding angles and corresponding sides.
Note:
* = 45o ^ = 160o
+ = 90o # = 75o
1.5 + # D C
3.5 A’ * 5
7.5 B’ ^
3.75 + # C’ D’
8.75

11. ✔ ✔ ✔ ✔ Corresponding Sides Corresponding Angles AB=2 A’B’=5 A=45o
BC=1.5
B’C’=3.75
B=160o
B’=160o
CD=3.5
C’D’=8.75
C=90o
C’=90o
DA=3
D’A’=7.5
D=75o
D’=75o A * 2 3 B ✔ ^
1.5 + # D C
3.5 A’ ✔ * 5 ✔ B’
7.5 ^ ✔
3.75 + # C’ D’
8.75

12. Corresponding Sides and their Proportions
AB=2
A’B’=5
BC=1.5
B’C’=3.75
CD=3.5
C’D’=8.75
DA=3
D’A’=7.5 A * 2 3 B ^ ✔
1.5 + # D C
3.5 A’ ✔ * 5 ✔ B’
7.5 ^ ✔
3.75 + # C’ D’
8.75

13. Corresponding Sides and their Proportions
Corresponding Angles
A=45o
A’=45o
B=160o
B’=160o
C=90o
C’=90o
D=75o
D’=75o
Corresponding Sides and their Proportions A * 2 3 B ^ ✔ ✔
1.5 + # D C
3.5 A’ ✔ ✔ * 5 ✔ ✔ B’
7.5 ^ ✔ ✔
So the corresponding angles are similar and the corresponding sides are proportional, so ABCD and A’B’C’D’ are similar polygons.
3.75 + # C’ D’
8.75

14. Solving Missing Sides
Where should we start?
What then?

15. Solving Missing Sides
First we need to determine the proportion between the two shapes.

16. Solving Missing Sides
Once we have our proportion, ratio, or scale factor, we can cross multiply to solve the remaining sides.

17. Solving Missing Sides

18. Solving Missing Sides

19. Solving Missing Sides

20. Solving Missing Sides

21. Assignment Time
Section 7.3 Pg
# 4a-b, 5a-b,6 - 9, 12,