Similar Triangles

Front

What are similar triangles?

Back

Triangles that have the same shape but may have different sizes. Their corresponding angles are equal, and their corresponding sides are in proportion.

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.

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.

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.

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.

Front

If the sides of triangle ABC are 3, 4, and 5, and triangle DEF is similar to triangle ABC with a scale factor of 2, what are the lengths of the sides of triangle DEF?

Back

The sides of triangle DEF are 6, 8, and 10.

Front

How do you find the missing side of a similar triangle?

Back

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

Front

If triangle GHI has sides 5, 12, and 13, and triangle JKL is similar to triangle GHI with a scale factor of 3, what are the side lengths of triangle JKL?

Back

The sides of triangle JKL are 15, 36, and 39.

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 ratio of the sides of two similar triangles is 1:4, what is the ratio of their areas?

Back

The ratio of their areas is 1:16.