Proving Similar Triangles #2

Front

What is the definition of similar triangles?

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are proportional.

Front

What is the Angle-Angle (AA) criterion for similarity?

Back

If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Front

What does it mean for corresponding angles to be congruent in similar triangles?

Back

It means that the angles in one triangle match in measure with the angles in another triangle, indicating that the triangles are similar.

Front

If triangle ABC is similar to triangle DEF, what can be said about their corresponding sides?

Back

The lengths of the corresponding sides of triangle ABC and triangle DEF are in proportion.

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 congruent 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, how do you find the length of a missing side?

Back

You can set up a proportion using the lengths of the corresponding sides of the similar triangles.

Front

What is the relationship between the ratios of the areas of two similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.

Front

If triangle XYZ is similar to triangle PQR and the length of side XY is 6 and side PQ is 9, what is the ratio of their corresponding sides?

Back

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

Front

What is the measure of the angles in similar triangles?

Back

The measures of the angles in similar triangles are equal.