Triangle Similarity

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What is Triangle Similarity?

Back

Triangle similarity refers to the concept that two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

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What is the similarity statement for two similar triangles?

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The similarity statement indicates that two triangles are similar, denoted as ΔABC~ΔDEF, meaning triangle ABC is similar to triangle DEF.

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What is the AA (Angle-Angle) Criterion for Triangle Similarity?

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The AA Criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

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What is the SSS (Side-Side-Side) Criterion for Triangle Similarity?

Back

The SSS Criterion states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

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What is the SAS (Side-Angle-Side) Criterion for Triangle Similarity?

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The SAS Criterion states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

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How do you find the value of x using proportions in similar triangles?

Back

Set up a proportion using the lengths of corresponding sides of the similar triangles and solve for x.

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What is a proportion?

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A proportion is an equation that states that two ratios are equal.

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If ΔXYZ~ΔNEW, what can be inferred about their angles?

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The corresponding angles of triangles XYZ and NEW are equal.

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If the sides of triangle ABC are 3, 4, and 5, and triangle DEF is similar to ABC with a scale factor of 2, what are the lengths of the sides of triangle DEF?

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The sides of triangle DEF are 6, 8, and 10.

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What is the relationship between the areas of two similar triangles?

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The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.