Similar Triangles

Front

What are similar triangles?

Back

Triangles that have the same shape but may have different sizes. Their corresponding angles are equal, and their corresponding sides are proportional.

Front

What is the criteria for triangles to be similar?

Back

Triangles are similar if: 1) AA (Angle-Angle) criterion: Two angles of one triangle are equal to two angles of another triangle. 2) SSS (Side-Side-Side) criterion: The sides of one triangle are proportional to the sides of another triangle. 3) SAS (Side-Angle-Side) criterion: Two sides of one triangle are proportional to two sides of another triangle, and the included angle is equal.

Front

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

Back

Their corresponding angles are congruent (equal in measure).

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 4 cm and side DE is 8 cm, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 1:2.

Front

What does it mean for sides in similar figures to be proportional?

Back

It means that the lengths of corresponding sides of the figures maintain a constant ratio.

Front

True or False: All angles in similar figures are congruent.

Back

True.

Front

True or False: The sides of similar triangles are equal in length.

Back

False. The sides are proportional, not necessarily equal.

Front

If triangle XYZ is similar to triangle PQR, and the lengths of sides XY and PQ are 5 cm and 10 cm respectively, what is the scale factor from triangle XYZ to triangle PQR?

Back

The scale factor is 2.

Front

How can you determine if two triangles are similar using the SSS criterion?

Back

By showing that the lengths of the corresponding sides of the triangles are in proportion.

Front

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

Back

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