Similar Triangles and Polygons

Is there a pattern?

3 cm

4 cm8 cm

6 cm12 cm

16 cm

Area: 12 cm2 Area:

48 cm2

Area: 192 cm2

Is there a pattern?

6 in

5 in

12 in

10 in 20 in

24 inArea:

15 in2 Area:

60 in2 Area:

240 in2

Practice:

8 m

12 m

Area: 96 m2

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?

Practice:

9 m

10 m

Area: 90 m2

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?

Is there a pattern?

5 cm

7 cm14 cm

10 cm20 cm

28 cm

Perimeter: 24 cm Perimeter:

48 cm Perimeter: 96 cm

Is there a pattern?

3 in

2 in

6 in

4 in 8 in

12 inPerimeter:

9 in

4 in8 in

16 in

Perimeter: 18 in

Perimeter: 36 in

Practice:

3 m

11 m

Area: 27 m

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?

Practice:

12 cm

9 cm

Area: 36 cm

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

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.

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.

Application:• Use the following rectangle to answer these

questions:

1. What is the perimeter of the rectangle?

2. What is the area of the rectangle?

3. If the length and width of the rectangle are tripled, how will the perimeter change?

5 inches

3 inches

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?

What size is the similar polygon?

• These two rectangles are similar and the ratio of their dimensions is 1:3. If the dimensions of the small rectangle are given, what are the dimensions of the large rectangle?

4 feet

2 feet

What size is the similar polygon?

• These two pentagons are similar and the ratio of their dimensions is 4:1. If the dimensions of the large pentagon are given, what are the dimensions of the small rectangle? 8 m

12 m

16 m

12 m

8 m

Application:

• A paper company has two sizes of poster board for sale. The dimensions of the smaller poster have a 1:2 to the large. If the smaller poster is 48 inches wide and 36 inches long, what are the dimensions of the larger poster board?

Challenge Question:

• Two similar triangles have a ratio of 1:2. If the dimensions of the small triangle are 10 ft, 10 ft, and 20 ft. What is the perimeter of the large triangle?

Challenge Question:

• Two similar triangles have a ratio of 5:1. If the dimensions of the large triangle are 50 ft, 50 ft, and 30 ft. What is the perimeter of the small triangle?