Triangle Similarity Conditions

Front

What is Triangle Similarity?

Back

Triangle similarity means that two triangles have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are proportional.

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What does AA Similarity stand for?

Back

AA Similarity stands for Angle-Angle Similarity. If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

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What does SSS Similarity stand for?

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SSS Similarity stands for Side-Side-Side Similarity. If the corresponding sides of two triangles are in proportion, the triangles are similar.

Front

What does SAS Similarity stand for?

Back

SAS Similarity stands for Side-Angle-Side Similarity. If two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, 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

Can two triangles be similar if they have no equal angles?

Back

No, if two triangles have no equal angles, they cannot be similar.

Front

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 ADB is similar to triangle AEC, what can be inferred about their angles?

Back

The corresponding angles of triangle ADB and triangle AEC are equal.

Front

What is the criterion for two triangles to be similar using only their angles?

Back

The AA criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

Front

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

Back

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