Similar Triangles

Front

What are similar triangles?

Back

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 criterion for triangle similarity?

Back

Two triangles are similar if their corresponding angles are equal (AA criterion) or if the lengths of their corresponding sides are proportional (SAS or SSS criteria).

Front

If triangle A is similar to triangle B, what can be said about their corresponding angles?

Back

The corresponding angles of triangle A and triangle B are congruent.

Front

If two triangles have sides in the ratio 2:3, are they similar?

Back

Not necessarily; we also need to check if their corresponding angles are equal.

Front

In similar polygons, what is true about the ratios of their corresponding sides?

Back

The ratios of their corresponding sides are proportional.

Front

What does it mean for two angles to be congruent?

Back

Two angles are congruent if they have the same measure.

Front

If triangle A has sides of lengths 3, 4, and 5, what are the lengths of the corresponding sides of a similar triangle with a scale factor of 2?

Back

The corresponding sides would be 6, 8, and 10.

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 side lengths.

Front

If triangle A is similar to triangle B and the length of a side in triangle A is 5, and the corresponding side in triangle B is 15, what is the scale factor?

Back

The scale factor is 3.

Front

What is the significance of the AA criterion in triangle similarity?

Back

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