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 similarity theorem?

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 similarity theorem?

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 similarity theorem?

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 determine if triangles are similar?

Back

Check for equal corresponding angles or proportional corresponding sides using AA, SSS, or SAS theorems.

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

If the sides of triangle ABC are 3, 4, and 5, and triangle DEF is similar to it with a side of 6, what is the length of the corresponding side in triangle DEF?

Back

The corresponding side in triangle DEF is 8 (using the ratio 6/3 = 2, so 4 * 2 = 8).

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.

Front

If two triangles are not similar, what can be concluded about their angles and sides?

Back

Their corresponding angles are not equal, and their corresponding sides are not in proportion.

Tags

CCSS.8.G.A.2

CCSS.HSG.CO.B.6

Front

What is the formula to find the length of a side in similar triangles?

Back

If triangle ABC ~ triangle DEF, then (AB/DE) = (BC/EF) = (AC/DF).

Tags

CCSS.HSG.SRT.A.2