Triangle Similarity

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What is Triangle Similarity?

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Triangle similarity refers to the relationship between two triangles that have the same shape but may differ in size. This means that their corresponding angles are equal and their corresponding sides are proportional.

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What does AA Similarity mean?

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AA Similarity (Angle-Angle Similarity) 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 does SSS Similarity mean?

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SSS Similarity (Side-Side-Side Similarity) states that if the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.

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What does SAS Similarity mean?

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SAS Similarity (Side-Angle-Side Similarity) states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

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If two triangles are similar, what can be said about their corresponding sides?

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The corresponding sides of similar triangles are proportional.

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What is the similarity statement for triangles ΔABC and ΔDEF if they are similar?

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ΔABC~ΔDEF.

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How can you prove that two triangles are similar using AA?

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To prove similarity using AA, show that two angles of one triangle are equal to two angles of another triangle.

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How can you prove that two triangles are similar using SSS?

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To prove similarity using SSS, show that the lengths of the corresponding sides of the two triangles are in proportion.

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How can you prove that two triangles are similar using SAS?

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To prove similarity using SAS, show that two sides of one triangle are proportional to two sides of another triangle and that the included angles are equal.

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What is the relationship between the areas of 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 sides.