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. SAS (Side-Angle-Side) Similarity: If two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, the triangles are similar. 3. SSS (Side-Side-Side) Similarity: If the corresponding sides of two triangles are in proportion, the triangles are similar.

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What does AA similarity criterion state?

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The AA similarity criterion states 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 SAS similarity criterion state?

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

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What does SSS similarity criterion state?

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

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If triangle ABC is similar to triangle DEF, what can be said about their angles?

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If triangle ABC is similar to triangle DEF, then angle A = angle D, angle B = angle E, and angle C = angle F.

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If triangle ABC has sides of lengths 3, 4, and 5, and triangle DEF has sides of lengths 6, 8, and 10, are the triangles similar?

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Yes, triangle ABC and triangle DEF are similar by the SSS similarity criterion, as the sides are in proportion (3:6, 4:8, 5:10).

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How can you prove that two triangles are not similar?

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To prove that two triangles are not similar, you can show that at least one of the similarity criteria (AA, SAS, SSS) does not hold true for the triangles.

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What is the relationship between the areas of similar triangles?

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The areas of similar triangles are proportional to the square of the lengths of their corresponding sides. If the ratio of the sides is a:b, then the ratio of the areas is a²:b².

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Can two triangles be similar if they have one angle equal and the other two angles different?

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No, two triangles cannot be similar if they have one angle equal and the other two angles different. For triangles to be similar, all corresponding angles must be equal.