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Applications of Similar Triangles

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question 1 of 3

Triangle HYV and triangle AYB are similar by the AA similarity theorem. What is the value of x?

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1. Given triangles DAR and KMR. What is the value of y?

2. Study the given diagram. Find the value of x, the distance between T and E.

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About This Quiz & Worksheet

Comparing the proportions of similar triangles can help you determine the length a given side that is dissimilar, and this quiz and worksheet will aid in your understanding by testing some of your basic algebra and geometry skills. To figure out the practice problems, you'll need to know about concepts like Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS) similarity theorems, and proportions.

Quiz & Worksheet Goals

In these assessments, you'll be tested on your understanding of:

  • The Angle-Angle similarity theorem and how to apply it to solve for a variable
  • Finding the length of a tree's shadow given the length of the tree, a nearby person and that person's shadow
  • Using fractions and cross-multiplying to determine proper proportion

Skills Practiced

  • Making connections - use understanding of the concept of using fractions and cross-multiplying to figure the unknown length of a triangle side
  • Defining key concepts - ensure that you can accurately define main phrases, such as congruent angles and triangle similarity
  • Problem solving - use acquired knowledge to solve the geometrical practice problems
  • Critical thinking - apply relevant concepts to examine information about triangles as applicable to real world scenarios in a different light

Additional Learning

To learn more about how to apply cross-multiplying to known triangle proportions in order to determine an unknown length, review the accompanying lesson on Applications of Similar Triangles. This lesson covers the following objectives:

  • Apply triangle similarity theorems to figure an unknown length
  • Understand proportions and congruent angles
  • Use cross-multiplying to determine the value of an unknown triangle length
  • Understand how this knowledge can help one solve real world problems
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