Similar Triangles

Front

What are similar triangles?

Back

Triangles that have the same shape but may differ in size. 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 is the AA criterion for triangle similarity?

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar (AA ~).

Tags

CCSS.HSG.SRT.A.2

Front

What is the SSS criterion for triangle similarity?

Back

If the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar (SSS ~).

Tags

CCSS.HSG.SRT.B.5

Front

What is the SAS criterion for triangle similarity?

Back

If two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar (SAS ~).

Tags

CCSS.HSG.SRT.B.5

Front

How do you find the missing side in similar triangles?

Back

Set up a proportion using the lengths of the corresponding sides of the triangles and solve for the missing side.

Tags

CCSS.HSG.SRT.A.2

Front

If ΔABC ∼ ΔDEF, and AB = 4, AC = 6, and DE = 8, what is the length of DF?

Back

DF = (DE/AB) * AC = (8/4) * 6 = 12.

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

Front

If two triangles have sides in the ratio 3:5, are they similar?

Back

Yes, if the corresponding angles are also equal, the triangles are similar.

Tags

CCSS.HSG.SRT.A.2

Front

What does it mean if two triangles are not similar?

Back

It means that their corresponding angles are not equal or their sides are not in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

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

Back

By showing that two angles of one triangle are equal to two angles of another triangle.

Tags

CCSS.HSG.SRT.A.2