Similar Triangles

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 relationship between the angles of similar triangles?

Back

The angles of similar triangles are congruent.

Front

If triangle ABC is similar to triangle DEF, what can be said about the sides AB, BC, and AC in relation to DE, EF, and DF?

Back

The sides AB, BC, and AC are proportional to the sides DE, EF, and DF respectively.

Front

What is the Side-Angle-Side (SAS) similarity criterion?

Back

If one angle of a triangle is congruent to one angle of another triangle and the sides including these angles are proportional, then the triangles are similar.

Front

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

Back

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

Front

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

Back

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

Front

What is the definition of proportional sides in similar polygons?

Back

In similar polygons, corresponding sides are proportional, meaning the ratios of the lengths of corresponding sides are equal.

Front

If triangle XYZ is similar to triangle PQR and XY = 4 cm, YZ = 6 cm, and PR = 8 cm, what is the length of QR?

Back

QR = (YZ/XY) * PR = (6/4) * 8 = 12 cm.

Front

What is the definition of congruent angles?

Back

Congruent angles are angles that have the same measure.

Front

In similar triangles, if the ratio of the lengths of two corresponding sides is 3:5, what is the ratio of their areas?

Back

The ratio of their areas is the square of the ratio of their corresponding sides, so (3/5)² = 9/25.