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 missing length in similar triangles?

Back

Set up a proportion using the lengths of corresponding sides and solve for the missing length.

Front

If triangle ABC is similar to triangle DEF, and AB = 10, DE = 5, what is the ratio of their sides?

Back

The ratio of their sides is 10:5 or 2:1.

Front

If two triangles are similar, how do their areas compare?

Back

The ratio of their areas is the square of the ratio of their corresponding sides.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

If the sides of triangle XYZ are 6, 8, and 10, and triangle PQR is similar to XYZ with a side of 4, what is the length of the corresponding side in triangle XYZ?

Back

The corresponding side in triangle XYZ is 6 (using the ratio 4:6).

Front

What is a scale factor in similar triangles?

Back

The ratio of the lengths of corresponding sides of two similar triangles.