Triangle Similarity Theorems

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What is the Triangle Similarity Theorem?

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The Triangle Similarity Theorem states that if two triangles have corresponding angles that are equal, then the triangles are similar, meaning their corresponding sides are in proportion.

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What does AA Similarity mean?

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AA Similarity (Angle-Angle Similarity) means 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 SAS Similarity mean?

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

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What is the Triangle Angle Bisector Theorem?

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The Triangle Angle Bisector Theorem states that the angle bisector of an angle in a triangle divides the opposite side into segments that are proportional to the other two sides.

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How do you set up proportions using the Triangle Angle Bisector Theorem?

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Which theorem states that if two triangles have one angle equal and the sides including those angles are in proportion, then the triangles are similar?

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This is known as the SAS Similarity Theorem.

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What is the significance of the AA Similarity Theorem in solving problems?

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The AA Similarity Theorem allows us to conclude that two triangles are similar if we can show that two pairs of corresponding angles are equal, simplifying many geometric problems.

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What is a common misconception about triangle similarity theorems?

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A common misconception is that ASA (Angle-Side-Angle) is a similarity theorem; however, it is not recognized as a separate theorem for triangle similarity.

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How can you determine if two triangles are not similar?

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If the corresponding angles are not equal or the sides are not in proportion, then the triangles are not similar.