similar triangles solving (overlap)

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, the triangles are similar.

Front

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

Back

Use the proportion of corresponding sides. If triangle A has sides a, b, c and triangle B has sides x, y, z, then a/x = b/y = c/z.

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

If two triangles are similar, what can be said about their areas?

Back

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

Front

How do you set up a proportion to solve for a missing side in similar triangles?

Back

Set up the proportion using corresponding sides: (side1 of triangle A)/(side1 of triangle B) = (side2 of triangle A)/(side2 of triangle B).

Front

If triangle ABC is similar to triangle DEF, and AB = 6, DE = 9, what is the ratio of their sides?

Back

The ratio of their sides is 6:9 or 2:3.

Front

What is the relationship between the corresponding angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If the lengths of the sides of triangle A are 4, 6, and 8, and triangle B is similar to triangle A with a side length of 12, what is the length of the corresponding side in triangle A?

Back

The corresponding side in triangle A is 8.