Similar Triangle Word Problems
1. Which of the following triangles are always similar? Explain your answer or give a counter-example (an example that shows they don’t have to be similar).
a. right triangles
b. isosceles triangles
c. equilateral triangles
2. The sides of a triangle are 5, 6 and 10. Find the length of the longest side of a similar triangle whose shortest side is 15.
3. Similar triangles are exactly the same shape and size. True or False? Explain.
4. Given: In the diagram,,BD= 4, DA= 6, andEC=8. Find BCto thenearest tenth.
5. Find BC
6. Two ladders are leaned against a wall such that they make the same angle with the ground. The 10' ladder reaches 8' up the wall. How much further up the wall does the 18' ladder reach?
7. At a certain time of the day, the shadow of a 5' boy is 8' long. The shadow of a tree at this same time is 28' long. How tall is the tree?
8. Two triangles are similar. The sides of the first triangle are 7, 9, and 11. The smallest side of the second triangle is 21. Find the perimeter of the second triangle.
9. Two triangular roofs are similar. The corresponding sides of these roofs are 16 feet and 24 feet. If the altitude of the smaller roof is 6 feet, find the corresponding altitude of the larger roof.
10. In triangle ABC, angle A = 90º and angle B = 35º. In triangle DEF, angle E = 35º and angle F = 55º. Are the triangles similar? Explain your answer.
11. Given angle A and angle A' are each 59º,
find AC.
12. A vertical flagpole casts a shadow 12 feet long at the same time that a nearby vertical post 8 feet casts a shadow 3 feet long. Find the height of the flagpole in feet.
For each of the following pictures with similar triangles, decide on a similarity ratio (larger to smaller) and then complete the problem using the one given side. Each problem should have a different similarity ratio. Solve your problem to show it works.
13.
Similarity Ratio: ______
14.
Similarity Ratio ______