1. Warm Up Solve each proportion. 1. 3 = 15 3. x 20 2. x 35 3 4 24 4 y 7= x 2. x 35 3 4 24 4 y 7 5

2. Dissections of Squares`
ACTIVITY 30min
Materials
Need glue & scissors
Dissections of Squares
Critical Thinking
Cut out each figure (one at a time) and rearrange pieces to form a square.
Glue pieces in the square provided.

3. Polygons and Similarities
6.1 and Chapter 7

4. 6.1 Properties and Attributes of Polygons
To identify and name polygons
To find the sum of the measures of interior and exterior angles of convex polygons and measures of interior and exterior angles of regular polygons
To solve problems involving angle measures of polygons

5. Define Polygons
A closed figure
Formed by segments

6. Polygons vs. Not Polygons

7. Regular Polygon
Convex polygon where all sides and angles are congruent.

8. Types of Polygons
A Convex polygon is a polygon such that no lines containing a side of the polygon contains a point in the interior of the polygon
~Angles face out
A Concave polygon is a polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon.
~ Angles cave in

9. Convex or Concave

10. Possible Diagonals/Triangles: Find the sum of degrees
Determine how many triangles a shape have by drawing diagonals. Each triangle is 180 degrees.

11. Thm 6-1-1: Polygon Angle Sum Theorem
Formula: S = 180 (n – 2)
S= sum of the measures of interior angles
N = number of sides
Sum
S = 180(n -2)
S = 180(3-2)
S = 180(1)
S = 180
An interior angle I = S/n
I = 180/3
I = 60

12. Thm6-1-2: Polygon Exterior Angle Sum Theorem
The sum of the measures of the exterior angles is 360°
To find one exterior angle use formula
Formula: E = 360/ n
E= measure of exterior angles
N = number of sides
E = 360/n
E = 360/3
E = 120

13. Warm-Up: Polygons Number of sides: Name Polygon: Number of Triangles:
Is polygon convex or concave.
Find sum of the measures of interior angles:
Find the measure of an interior angle
Find measure of an exterior angle: 6
Hexagon
(n- 2)
= 4
S = 180(n-2)
180(4)= 720
I = Sum n
720 = 120 6
360 = 60 6
E = 360 n

14. Twitter #polygonsproperties
P. 397 Think and Discuss #1
Draw a concave pentagon and convex pentagon. Explain the difference between the two figures.

15. Measure of an Exterior Angle
Textbook p. 395
Convex Polygons
Number of Sides
Number of triangles
Sum of Angles Measures
S = 180(n – 2)
Measure of an Exterior Angle
Ext = 360/n
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
n - gon n
(n – 2)
S = 180( n – 2)
Ext = 360 / n

16. Practice
Geo: Textbook page 398 # 1- 15

17. Warm-Up: Polygons Number of sides: Name Polygon: Number of Triangles:
Is polygon convex or concave.
Find sum of the measures of interior angles:
Find the measure of an interior angle
Find measure of an exterior angle: 7
Heptagon
(n- 2)
= 5
S = 180(n-2)
180(5)= 900
I = Sum n
900 = 7
360 = 51.43 7
E = 360 n

18. Warm Up: Part 2 Solve each proportion. 1. x = 11 2. 13 = 26 3. x-2 = 3
Cross Multiply
- 35(x) = 11(5)
- 35x = 55
35x = 55
- x = 1.57
Cross Multiply
- 13(7x) = 49(26)
x = 1274
91x = 1274
- x = 14
Cross Multiply
- 8(x-2) = 3(x)
- 8x -16 = 3x
8x -8x -16 = 3x – 8x
= -5x
-16 = -5x
- x = 3.2

19. Practice
Geo: Textbook page 398 # 1- 15

20. Chapter 7: Connecting Proportion and Similarity
Recognize and use ratios and proportions
Identify similar figures and use the proportions of similar figures to solve problems
Use proportional parts of triangles to solve problems

21. Exploring Similar Polygons
Book Definition:
Two polygons are similar if and only if their corresponding angles are congruent and the measures of their corresponding sides are proportional.
Symbol:
In simpler terms:
Two polygons with the same shape but are different sizes.

22. Are two congruent figures similar?
Think about it….
Discuss…
Yes, congruent figures have congruent angles and sides are proportional at 1:1 ratio

23. Scale Factor and Dilation
Dilation is a transformation that reduces or enlarges figures
On a camera: zoom-in/ zoom-out
Scale Factor = ______
A D
B C
E H
dfgff
F G
10 = 5
8 = 4
6 = 3 5
2.5

24. Scale Factor Scale Factor = _____ 4 8 3 12 24 9 Scale Factor = ______
A D
B C
E H
dfgff
F G
12 = 4
9 = 3 24 8
12 = 6
8 = 5
7 = 4 4 2

25. Similar Triangles: Property 1
__________________________:
if _____________________ of one triangle are
____________ to __________________________ of
another triangle, then the triangles are ____________.
Ex.
Side-Side-Side Similarity
the three sides
proportional
the three corresponding sides
similar

26. Similar Triangles: Property 2
Angle - Angle Similarity
_________________________:
If the measures of ___________ of ___________
are __________________________________
then the triangles are __________.
Ex.
two angles
one triangle
congruent to 2 angles of the other
similar

27. Similar Triangles: Property 3
Side-Angle-Side Similarity
________________________:
if the measures of __________ of a triangle are ___________
to the measures of _________ of another triangle and the
_________ angles are _________, then the triangles are
___________.
Ex.
two sides
proportional
two sides
included
congruent
similar

29. Similarity Ratio:

30. Triangle Proportionality Theorem
VW = VX
WY XZ

31. Similarity Ratio:
AE = AD = ED
AC AB CB

32. Similarity Ratio:
EC = ED = CD
EA EB AB X

33. Solve for x and y. x
y+3 21

34. Warm- up: 1. Draw a convex heptagon. 2. Draw a concave nonagon
3. Sketch a regular hexagon.
Sum of interior angles:
An Interior angle:
An Exterior angle:
S = 180(6-2) = 720
I = 720/6 = 120
E = 360/6 = 60

35. Check Practice: Similar Figures
Notes: Sides are proportional & angles are congruent.
P. 520 # 5, 6, 12, 13, 16, 17, 19

36. Quiz Time 10 mins Absolutely NO TALKING during quiz. Take your time
Good LUCK!

37. Practice Find a partner.
Complete “How Can You Tell Which End of a Worm Is His Head?” (must complete in pairs).
Each partner complete a side
For each answer, write in letter of question. EACH SIDE IS DIFFERENT!
Each partner must show work to receive FULL CREDIT. Use notebook paper

38. Chapter 7: Practice

39. Warm-Up
1. Use the Interior Angle Theorem to find measure of each angle C
B x-12
4x-14
A 7x x -15 D 5x E
2. Are two congruent figures similar? Explain.
3. Quadrilaterals ABCD and AEFG are similar. AE=22, AB=5x + 4, EF=8 and BC=2x-2. Solve for x.
A E B
G F
D C

40. Warm -Up 16 22
11 m 3 8 4 4 x

41. Warm up 2. What is the difference between concave and convex polygons?
3. regular heptagon, find each.
A. Sum of I =
B. I=
C. E=
D. Sum of E=
1. Similar? Yes or No a
1.4 7 b 5
12.5

42. Constructions Materials: paper, ruler and protractor
Construct each (use polygon chart)
Regular Pentagon ~ sides 3 inches
Regular Octagon ~ sides 2 inches
Your Choice ~ Regular Polygon ~ make sides a reasonable measure
To start… find the measure of one interior angle. Draw one measured side with ruler.
Next use protractor to measure angle
Then draw 2nd side
Repeat steps.

43. Practice: Constructions
Construct each (use polygon chart)
Materials: paper, ruler and protractor
Include the sum of interior angles and the measure of one interior angle
Regular Pentagon ~ sides 3 inches
Regular Octagon ~ sides 2 inches
Your Choice ~ Regular Polygon (4+ sides) ~ make sides a reasonable measure
Bonus: Your Choice ~ Regular Polygon (4+ sides) ~ make sides a reasonable measure
To start… Draw one measured side with ruler.
Next find the measure of one interior angle and use protractor to measure interior angle
Then draw 2nd side
Repeat steps.

44. Warm up 2. What is the difference between concave and convex polygons?
3. regular heptagon, find each.
A. Sum of I =
B. I=
C. E=
D. Sum of E=
1. Similar? Yes or No a
1.4 7 b 5
12.5

45. Bonus
1. Draw if needed. Joyce sighted to the top of a tree along a stake that she knew to be 3 feet high. If she is standing 2 feet from the stake and 18 feet from the tree, how high is the tree?
2. Find x.
2x x+5
10x x+3
4x x+2
3. The lengths of the sides of a triangle are 3, 4, and 6. If the length of the shortest side of a similar triangle is 5, find the lengths of its other two sides.