Find Missing Sides and Angles of 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 sides and angles.
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More topics on similar triangles
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
1. Corresponding angles must have the same measure.
2. Corresponding sides must be proportional. (That is the ratios of their corresponding sides must be equal)
Examples:
1. The two triangles are similar. Determine the measure of angle A and angle B.
2. The two triangles are similar. Determine the length of the sides DE and EF.
3. 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.
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.
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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