Triangle Similarity

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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 that their corresponding angles are equal and their corresponding sides are proportional.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

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What does AA Similarity mean?

Back

AA Similarity (Angle-Angle Similarity) states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Tags

CCSS.HSG.SRT.A.2

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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 proportional to the three sides of another triangle, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What does SAS Similarity mean?

Back

SAS Similarity (Side-Angle-Side Similarity) 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.

Tags

CCSS.HSG.SRT.B.5

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

Back

The corresponding sides of similar triangles are proportional.

Tags

CCSS.HSG.SRT.A.2

Front

What is the similarity statement for triangles ΔABC and ΔDEF if they are similar?

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ΔABC~ΔDEF.

Tags

CCSS.HSG.SRT.A.2

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How can you prove that two triangles are similar using AA?

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To prove similarity using AA, show that two angles of one triangle are equal to two angles of another triangle.

Tags

CCSS.HSG.SRT.B.5

Front

How can you prove that two triangles are similar using SSS?

Back

To prove similarity using SSS, show that the lengths of the corresponding sides of the two triangles are in proportion.

Tags

CCSS.HSG.SRT.B.5

Front

How can you prove that two triangles are similar using SAS?

Back

To prove similarity using SAS, show that two sides of one triangle are proportional to two sides of another triangle and that the included angles are equal.

Tags

CCSS.HSG.SRT.B.5

Front

What is the relationship between the areas of similar triangles?

Back

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