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 stand for in triangle similarity?

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AA stands for Angle-Angle similarity criterion. If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

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What does SAS stand for in triangle similarity?

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SAS stands for Side-Angle-Side similarity criterion. If two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, the triangles are similar.

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What does SSS stand for in triangle similarity?

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SSS stands for Side-Side-Side similarity criterion. If the corresponding sides of two triangles are proportional, then the triangles are similar.

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

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The corresponding angles of similar triangles are equal.

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

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To prove similarity using the AA criterion, 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 the SAS criterion?

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To prove similarity using the SAS criterion, 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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How can you prove that two triangles are similar using the SSS criterion?

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

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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 sides.