Find Missing Sides and Angles of Similar Triangles
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More topics on similar triangles
Videos, worksheets, examples, and solutions to help Grade 8 students learn how to find missing sides and angles of similar triangles.
Similar Triangles
Similar triangles are triangles that have exactly the same shape, but are not necessarily the same size. When two triangles are similar, the ratios of the lengths of their corresponding sides are equal. We can use these properties of similar triangles to find missing side lengths or heights in real-world problems (like shadow measurements, map scaling, or indirect height calculations).
The following diagrams show how to use similar triangles to find the height of a tree. Scroll down the page for more examples and solutions.
Geometry Worksheets
Practice your skills with the following worksheets:
Printable & Online Geometry Worksheets
Steps to Find Missing Measures Using Similar Triangles:
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Identify Similar Triangles
Look for two triangles where:
All corresponding angles are equal (AA Similarity), or
Two sides are proportional and the included angles are equal (SAS), or
All three sides are proportional (SSS). -
Set Up a Proportion
Since corresponding sides are proportional:
\(\frac{\text{Side in Triangle A}}{\text{Corresponding Side in Triangle B}}=\frac{\text{Unknown Side in Triangle A}}{\text{Corresponding Side in Triangle B}}\) -
Solve the Proportion:
Use cross-multiplication or other algebraic methods to solve for the unknown variable.
Congruent and Similar Triangles
Determine congruent and similar triangles. Use similar triangles to solve problems.
Congruent triangles have the same size and the same shape. Corresponding sides are the same length and the corresponding angles are congruent.
Similar triangles have the exact same shape but not necessarily the same size.
The conditions for similarity are
- Corresponding angles must have the same measure.
- Corresponding sides must be proportional. (That is the ratios of their corresponding sides must be equal)
Examples: - The two triangles are similar. Determine the measure of angle A and angle B.
- The two triangles are similar. Determine the length of the sides DE and EF.
- A tree casts a shadow 45 feet long. At the same time, the shadow cast by a vertical 3 ft stick is 5 ft long. Find the height of the tree.
Solving for Unknown Values Using the Properties of Similar Triangles
This video shows examples of determining unknown values using the properties of similar triangles.
Indirect Measurement Using Similar Triangles
This video explains how to use the properties of similar triangles to determine the height of a tree.
Similar Triangles
Students review the idea that the ratios of the lengths of corresponding sides of similar figures are equal. Students then use this idea to find missing segment lengths in similar figures.
Similar Triangles - Find the missing side.
Proportions with similar figures - find the missing length.
How to find a missing part of a triangle that is similar to another triangle?
How to find a missing part of a triangle that is similar to another triangle?
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