Similarity

  1. A student shines a light through a cutout of a triangle held parallel to a wall several feet straight in front of him, producing a similar image on the wall.

What must the two triangles have in common?

  1. equal areas
  2. equal heights
  3. corresponding sides that are congruent
  4. corresponding angles that are congruent
  1. Alanis is moving and needs to pack two mirrors. The larger mirror fits in a box that is 18 inches wide by 20 inches long. Her smaller mirror is similar in proportion to the larger mirror. Alanis determines that the width of the smaller box needs to be at least 9 inches. What should be the minimum length of the box to hold the smaller mirror?
  1. 2 inches
  2. 6 inches
  3. 9 inches
  4. 10 inches
  1. The shadow cast by a one-foot ruler is 8 inches long. At the same time, the shadow cast by a pine tree is 24 feet long.

What is the height, in feet, of the pine tree?

  1. 3 feet
  2. 16 feet
  3. 36 feet
  4. 192 feet
  1. Alicia is 5 feet tall. She casts a shadow that measures 6 feet long at the same time that a sculpture in the park casts a shadow 12 feet long.

Which of the following is the approximate height of the sculpture?

A.9 feet

B. 16 feet

C.27 feet

D.78 feet

  1. The ratio of the side lengths of a quadrilateral is 6:2:3:7, and its perimeter is 126 meters. What is the length of the shortest side?
  1. Solve the proportion: (Show all work!)

What is the measure of angle D?

  1. 37°
  2. 45°
  3. 53°
  4. 74°
  1. Always, sometimes or never true? Two pentagons that are congruent, are similar.
  1. Always, sometimes or never true? Two isosceles right triangles are similar.
  1. Always, sometimes or never true? Two equilateral triangles are similar.
  1. Always, sometimes or never true? A square and a rectangle are similar.
  1. An airline executive drew a sketch of a logo on a napkin.

She gave the logo to a graphic designer so he could make a mathematically similar version with a computer drawing program. The center line of the new logo needs to be 10 centimeters long. Which of these proportions could the graphic designer use to find the value of y?

  1. and are both perpendicular to . In triangle ABC, the length of is 4 cm and the length of is 2 cm.

If the length of is 8 cm, what is the length of ?

  1. 4 cm
  1. 16 cm
  1. Before her trip to Canada, Liz exchanged 300 U.S. dollars for Canadian dollars at a rate of 1 U.S. dollar to 1.35 Canadian dollars.

When Liz arrived in Canada, the exchange rate was 1 Canadian dollar to 0.76 U.S. dollars.

  • Determine the amount of money in Canadian dollars that Liz received for her 300 U.S. dollars.
  • Determine whether Liz would have received more Canadian money for her 300 U.S. dollars if she had waited to exchange her money in Canada.

Show your work or provide an explanation for your answers.

  1. Similar trapezoids are shown.

What is the value of n?

  1. 10
  2. 12
  3. 15
  4. 19
  1. Explain why the triangles are similar and write a similarity statement.
  1. Determine whether the polygons are similar. If so, write the similarity ratio and a similarity statement.
  1. To find out how wide a river is, John and Sally mark an X at the spot directly across from a big rock on the other side of the river. Then they walk in a straight line along the river, perpendicular to the straight line between the X and the rock. After walking for 20 feet Jon stops while Sally continues along the straight line for another 10 feet. Then she makes a 90 degree turn and walks for 30 feet. When she stops and looks at the rock she sees that the straight line from her to the rock passes through John. What is the distance from X to the rock?
  1. Find .
  1. State if the triangles are similar. If so, state how you know they are similar and write the similarity statement.