Triangle Similarity and Congruence

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What is Triangle Similarity?

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Triangle similarity occurs when two triangles have the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are in proportion.

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What is Triangle Congruence?

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Triangle congruence means that two triangles are identical in shape and size. This implies that all corresponding sides and angles are equal.

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What is the AA Criterion for Similarity?

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The AA (Angle-Angle) 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 Criterion for Congruence?

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The SSS (Side-Side-Side) Criterion states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

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What is the SAS Criterion for Congruence?

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The SAS (Side-Angle-Side) Criterion states that if two sides of one triangle are equal to two sides of another triangle and the included angle is equal, then the triangles are congruent.

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How do you find a missing side in similar triangles?

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To find a missing side in similar triangles, set up a proportion using the lengths of the corresponding sides of the triangles.

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What is the relationship between corresponding angles in similar triangles?

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In similar triangles, corresponding angles are equal.

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What is the relationship between corresponding sides in similar triangles?

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In similar triangles, the lengths of corresponding sides are proportional.

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

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The areas of two similar triangles are in the ratio of the square of the lengths of their corresponding sides.

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What is the formula for the area of a triangle?

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The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.