Similar Triangles

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are proportional.

Front

What is the relationship between the sides of similar triangles?

Back

The sides of similar triangles are proportional, meaning the ratios of the lengths of corresponding sides are equal.

Front

Are all angles in similar triangles congruent?

Back

Yes, all corresponding angles in similar triangles are congruent.

Front

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

Back

The ratios of the lengths of corresponding sides are equal, i.e., \( \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} \).

Front

If two triangles have one angle equal and the sides including that angle proportional, what can be concluded?

Back

The two triangles are similar by the Angle-Angle (AA) similarity criterion.

Front

What is the AA similarity criterion?

Back

The AA similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

Back

Front

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

Back

The ratio of their corresponding sides is \( \frac{XY}{PQ} = \frac{6}{9} = \frac{2}{3} \).

Front

What is the SSS similarity criterion?

Back

The SSS similarity criterion states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

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

Back

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