Target 5-A, Target 5-B, Target 5-C

Target 5-A

  

Understand the proportional relationship between two similar figures.

  • Use proportions to find missing lengths of similar figures.
  • Use proportions to find areas and volumes of similar figures.
  • Use proportions to solve problems.
  • Use algebraic reasoning to solve proportions.

 

 

Sample Questions

  1. Triangles CAT and DOG are similar. The scale factor from ΔCAT to ΔDOG is 2/3.
    1. Draw a picture to show what these triangles might look like.
    2. Complete this proportion:
    3. What is the ratio of the areas of ΔCAT and ΔDOG ?

  2. ΔARM and ΔLEG shown below are similar. Find the values of x and y.
  3. ΔABC ~ ΔPQR as shown below. Write a proportion and find the value of x.
  4. A tree casts a 40 foot shadow. At the same time Joe, who is 6 ft 3 inches tall, casts an 8 ft. shadow. Draw a diagram to represent the situation, and use proportional reasoning to find the height of the tree.

Sample Response
  1. Triangles CAT and DOG are similar. The scale factor from ΔCAT to ΔDOG is 2/3.
    1. Draw a picture to show what these triangles might look like.
    2. Complete this proportion:
    3. What is the ratio of the areas of ΔCAT and ΔDOG ? The ratio is (2/3)2 = 4/9.

  2. ΔARM and ΔLEG shown below are similar. Find the values of x and y.

    12/16 = x/24 so x = 18.
    12/16 = 15/y so y = 20.
  3. ΔABC ~ ΔPQR as shown below. Write a proportion and find the value of x.

  4. A tree casts a 40 foot shadow. At the same time Joe, who is 6 ft 3 inches tall, casts an 8 ft. shadow. Draw a diagram to represent the situation, and use proportional reasoning to find the height of the tree.

    The shadow of the tree is 5 times that of Joe. So the height of the tree must be 5*(6.25) = 31.25. So the tree is 31.25 feet tall which is 31 feet 3 inches.