Triangle Similarity

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What is Triangle Similarity?

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Triangle similarity refers to the property of two triangles having the same shape but not necessarily the same size. This means that their corresponding angles are equal and their corresponding sides are in proportion.

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What are the criteria for triangle similarity?

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The three main criteria for triangle similarity are: 1. AA (Angle-Angle) Similarity: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. 2. SSS (Side-Side-Side) Similarity: If the sides of one triangle are proportional to the sides of another triangle, the triangles are similar. 3. SAS (Side-Angle-Side) Similarity: If two sides of one triangle are proportional to two sides of another triangle and the included angle is equal, the triangles are similar.

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What does AA Similarity mean?

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AA Similarity means that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

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What does SSS Similarity mean?

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SSS Similarity means that if the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar.

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What does SAS Similarity mean?

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SAS Similarity means that if two sides of one triangle are proportional to two sides of another triangle and the included angle between those sides is equal, then the triangles are similar.

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If two triangles have one angle equal and the sides including that angle are in proportion, what can be concluded?

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The triangles are similar by the SAS (Side-Angle-Side) criterion.

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If two triangles have two angles equal, what can be concluded?

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The triangles are similar by the AA (Angle-Angle) criterion.

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If two triangles have all three sides in proportion, what can be concluded?

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The triangles are similar by the SSS (Side-Side-Side) criterion.

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Can two triangles be similar if only one angle is equal?

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No, two triangles cannot be similar if only one angle is equal. At least two angles must be equal (AA criterion) for similarity.

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What is the relationship between the angles of similar triangles?

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The corresponding angles of similar triangles are equal.