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 Angle-Angle (AA) criterion for similarity?

Back

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

Tags

CCSS.HSG.SRT.A.2

Front

What is the Side-Side-Side (SSS) criterion for similarity?

Back

If the corresponding sides of two triangles are in proportion, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

What is the Side-Angle-Side (SAS) criterion for similarity?

Back

If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in proportion, then the triangles are similar.

Tags

CCSS.HSG.SRT.B.5

Front

If triangle A has sides of length 3, 4, and 5, and triangle B has sides of length 6, 8, and 10, are they similar?

Back

Yes, because the sides of triangle B are twice the length of the corresponding sides of triangle A.

Tags

CCSS.HSG.SRT.A.2

Front

How do you find the missing side of similar triangles?

Back

Use the proportion of the corresponding sides to set up a ratio and solve for the missing side.

Tags

CCSS.HSG.SRT.A.2

Front

If triangle A has angles of 30°, 60°, and 90°, what are the angles of a similar triangle?

Back

30°, 60°, and 90° (the angles remain the same in similar triangles).

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

What does it mean if two triangles are not similar?

Back

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

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

If triangle A has a side of length 5 and triangle B has a corresponding side of length 10, what is the scale factor?

Back

The scale factor is 2.

Tags

CCSS.7.G.A.1

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.