Similar Triangles and Polygons

1
Similar Triangles and Polygons
2
Is there a pattern?
4 cm
8 cm
16 cm
3 cm
6 cm
Area 12 cm2
12 cm
Area 48 cm2
Area 192 cm2
3
Is there a pattern?
5 in
10 in
20 in
6 in
12 in
Area 15 in2
24 in
Area 60 in2
Area 240 in2
4
Practice
If we double the length of the sides of this
rectangle, what would be the new dimensions?
What would the area of the new rectangle be?
12 m
8 m
Area 96 m2
5
Practice
If we double the length of the sides of this
rectangle, what would be the new dimensions?
What would the area of the new rectangle be?
10 m
9 m
Area 90 m2
6
Is there a pattern?
7 cm
14 cm
28 cm
5 cm
10 cm
Perimeter 24 cm
20 cm
Perimeter 48 cm
Perimeter 96 cm
7
Is there a pattern?
4 in
2 in
8 in
4 in
16 in
8 in
3 in
6 in
Perimeter 9 in
12 in
Perimeter 18 in
Perimeter 36 in
8
Practice
If we double the length of the sides of this
rectangle, what would be the new dimensions?
What would the perimeter of the new rectangle be?
11 m
3 m
Area 27 m
9
Practice
If we double the length of the sides of this
triangle, what would be the new dimensions? What
would the perimeter of the new triangle be?
15 cm
9 cm
12 cm
Area 36 cm
10
Application

• What would happen to the perimeter of a similar
  triangle if the length of the sides were tripled?
  Justify by drawing a picture and showing the
  math.

11
Application

• If the length and width of a rectangle are
  multiplied by 5, how does the area change?
  Justify by drawing a picture and showing the
  math.

12
Application

• Use the following rectangle to answer these
  questions
• What is the perimeter of the rectangle?
• What is the area of the rectangle?
• If the length and width of the rectangle are
  tripled, how will the perimeter change?

5 inches
3 inches
13
Challenge Question

• A rug company has two sizes of rugs for sale.
  The length and width of the larger rug are twice
  the dimensions of the smaller one. The area of
  the larger rug is 96 ft2. What is the area of
  the smaller rug?

14
What size is the similar polygon?

• These two rectangles are similar and the ratio of
  their dimensions is 13. If the dimensions of
  the small rectangle are given, what are the
  dimensions of the large rectangle?

2 feet
4 feet
15
What size is the similar polygon?

• These two pentagons are similar and the ratio of
  their dimensions is 41. If the dimensions of
  the large pentagon are given, what are the
  dimensions of the small rectangle?

8 m
8 m
12 m
12 m
16 m
16
Application

• A paper company has two sizes of poster board for
  sale. The dimensions of the smaller poster have
  a 12 to the large. If the smaller poster is 48
  inches wide and 36 inches long, what are the
  dimensions of the larger poster board?

17
Challenge Question

• Two similar triangles have a ratio of 12. If
  the dimensions of the small triangle are 10 ft,
  10 ft, and 20 ft. What is the perimeter of the
  large triangle?

18
Challenge Question

• Two similar triangles have a ratio of 51. If
  the dimensions of the large triangle are 50 ft,
  50 ft, and 30 ft. What is the perimeter of the
  small triangle?