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) similarity criterion?

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) similarity criterion?

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) similarity criterion?

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 ABC is similar to triangle DEF, and the lengths of sides AB and DE are 4 cm and 8 cm respectively, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Tags

CCSS.HSG.SRT.A.2

Front

How do you find a missing side in similar triangles?

Back

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

Tags

CCSS.HSG.SRT.A.2

Front

Back

h = 50.

Front

If triangle XYZ is similar to triangle PQR, and XY = 6 cm, YZ = 9 cm, and PQ = 12 cm, what is the length of QR?

Back

QR = 18 cm.

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 the sides of two similar triangles are in the ratio 3:5, what is the ratio of their areas?

Back

The ratio of their areas is 3^2:5^2 or 9:25.