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

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

What does AA stand for in triangle similarity?

Back

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

Tags

CCSS.HSG.SRT.B.5

Front

What does SAS stand for in triangle similarity?

Back

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

Tags

CCSS.HSG.SRT.B.5

Front

What does SSS stand for in triangle similarity?

Back

SSS stands for Side-Side-Side similarity criterion. If the corresponding sides of two triangles are proportional, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

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

Back

The corresponding angles of similar triangles are equal.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

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

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

Back

To prove similarity using the AA criterion, 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 the SAS criterion?

Back

To prove similarity using the SAS criterion, 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

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

Back

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

Tags

CCSS.HSG.SRT.B.5

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.