Solving 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.

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.

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.

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.

Front

How do you find the length of a side in similar triangles?

Back

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

Front

If triangle ABC is similar to triangle DEF, and AB = 4, AC = 6, and DE = 8, what is the length of DF?

Back

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

Front

What is the ratio of the areas of two similar triangles?

Back

The ratio of the 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 3²:5² = 9:25.

Front

How can you determine if two triangles are similar using their angles?

Back

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

Front

What is a scale factor in similar triangles?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar triangles.