Triangle Similarity: AA, SAS, SSS

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 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 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 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

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

If two triangles have angles measuring 30°, 60°, and 90°, are they similar?

Back

Yes, they are similar by AA since all corresponding angles are equal.

Tags

CCSS.HSG.SRT.A.2

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, they are similar by SSS because the sides are in proportion (3:6, 4:8, 5:10).

Tags

CCSS.HSG.SRT.A.2

Front

How do you determine if two triangles are similar using the AA criterion?

Back

To determine similarity using the AA criterion, check if two angles of one triangle are equal to two angles of another triangle.

Tags

CCSS.HSG.SRT.A.2

Front

What is the relationship between the sides of similar triangles?

Back

The corresponding sides of similar triangles are in proportion, meaning the ratios of the lengths of corresponding sides are equal.

Tags

CCSS.HSG.SRT.A.2

Front

If triangle GHI is similar to triangle JKL, and GH = 5, JK = 10, what is the ratio of their sides?

Back

The ratio of their sides is 1:2, since 5:10 simplifies to 1:2.

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