Triangle Similarity

Front

What is Triangle Similarity?

Back

Triangle similarity refers to the property of two triangles having the same shape but not necessarily the same size. This means that their corresponding angles are equal and their corresponding sides are in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

What are the criteria for triangle similarity?

Back

The three main criteria for triangle similarity are: 1. AA (Angle-Angle) Similarity: If two angles of one triangle are equal to two angles of another triangle, the triangles are similar. 2. SSS (Side-Side-Side) Similarity: If the sides of one triangle are proportional to the sides of another triangle, the triangles are similar. 3. SAS (Side-Angle-Side) Similarity: If two sides of one triangle are proportional to two sides of another triangle and the included angle is equal, the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What does AA Similarity mean?

Back

AA Similarity means that if two angles of one triangle are equal to two angles of another triangle, then the two triangles are similar.

Tags

CCSS.HSG.SRT.A.2

Front

What does SSS Similarity mean?

Back

SSS Similarity means that if the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What does SAS Similarity mean?

Back

SAS Similarity means that if two sides of one triangle are proportional to two sides of another triangle and the included angle between those sides is equal, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

If two triangles have one angle equal and the sides including that angle are in proportion, what can be concluded?

Back

The triangles are similar by the SAS (Side-Angle-Side) criterion.

Tags

CCSS.HSG.SRT.B.5

Front

If two triangles have two angles equal, what can be concluded?

Back

The triangles are similar by the AA (Angle-Angle) criterion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

If two triangles have all three sides in proportion, what can be concluded?

Back

The triangles are similar by the SSS (Side-Side-Side) criterion.

Tags

CCSS.HSG.SRT.A.2

Front

Can two triangles be similar if only one angle is equal?

Back

No, two triangles cannot be similar if only one angle is equal. At least two angles must be equal (AA criterion) for similarity.

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Tags

CCSS.HSG.SRT.A.2