Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the relationship between two triangles that have the same shape but may differ in size. This means their corresponding angles are equal and their corresponding sides are proportional.

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What does AA stand for in triangle similarity?

Back

AA stands for Angle-Angle similarity criterion, which 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 does SAS stand for in triangle similarity?

Back

SAS stands for Side-Angle-Side similarity criterion, which states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then 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, which states that if the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

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

Back

The corresponding sides of similar triangles are proportional.

Front

If triangle A is similar to triangle B, what can be said about their angles?

Back

The corresponding angles of similar triangles are equal.

Front

Can two triangles be similar if only one pair of angles is equal?

Back

No, two triangles cannot be similar if only one pair of angles is equal; at least two pairs of angles must be equal.

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What is the relationship between the areas of two similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Front

If triangle A has sides of lengths 3, 4, and 5, and triangle B has sides of lengths 6, 8, and 10, are they similar?

Back

Yes, triangle A and triangle B are similar because the sides are proportional (3:6, 4:8, 5:10).

Front

What is the significance of the similarity criteria in solving problems?

Back

The similarity criteria (AA, SAS, SSS) help determine whether two triangles are similar, which is essential for solving various geometric problems.