Similar Triangles/Side Splitter/Ratio

Front

What are similar triangles?

Back

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

Front

What is the Side Splitter Theorem?

Back

If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

How do you find the ratio 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 two triangles are similar, what can be said about their corresponding angles?

Back

All corresponding angles in similar triangles are congruent.

Front

What is the formula for finding the length of a side in similar triangles?

Back

If triangle ABC is similar to triangle DEF, then the ratio of the lengths of corresponding sides is equal: AB/DE = AC/DF = BC/EF.

Front

If the sides of two similar triangles are in the ratio 3:4, what is the ratio of their areas?

Back

The ratio of their areas is 3²:4², which simplifies to 9:16.

Front

What is a proportional relationship in the context of similar triangles?

Back

A proportional relationship means that the ratios of corresponding sides of similar triangles are equal.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if they satisfy one of the following criteria: AA (Angle-Angle), SSS (Side-Side-Side), or SAS (Side-Angle-Side) similarity.

Front

What is the significance of the corresponding sides in similar triangles?

Back

The lengths of corresponding sides of similar triangles are in proportion, which allows for the calculation of unknown lengths.

Front

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

Back

The ratio of AB to DE is 6:9, which simplifies to 2:3.