Similar Triangles Theorems

Front

What does AA stand for in triangle similarity?

Back

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

Tags

CCSS.HSG.SRT.A.2

Front

What does SSS stand for in triangle similarity?

Back

SSS stands for Side-Side-Side. If the corresponding sides of two triangles are in proportion, 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. If two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

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.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

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

Back

The triangles are similar by the AA criterion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

What is the criterion for similarity using SSS?

Back

If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What is the criterion for similarity using SAS?

Back

If two sides of one triangle are proportional to two sides of another triangle and the included angle is equal, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

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

Back

Their corresponding sides are in proportion.

Tags

CCSS.HSG.SRT.A.2

Front

If triangle ABC is similar to triangle DEF, what can be said about their angles?

Back

Angle A = Angle D, Angle B = Angle E, Angle C = Angle F.

Tags

CCSS.HSG.SRT.A.2

Front

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

Back

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