Similarity Statements

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.

Front

What is a similarity statement?

Back

A similarity statement is a mathematical statement that indicates that two figures are similar, often written in the form of \( \Delta ABC \sim \Delta DEF \).

Front

If \( \Delta ABC \sim \Delta DEF \), what can we say about their angles?

Back

The corresponding angles are congruent: \( \angle A \cong \angle D, \angle B \cong \angle E, \angle C \cong \angle F \).

Front

If two triangles are similar, what can we say about their sides?

Back

The lengths of their corresponding sides are proportional.

Front

What is the relationship between congruent triangles and similar triangles?

Back

All congruent triangles are similar, but not all similar triangles are congruent.

Front

What does it mean for corresponding sides to be proportional?

Back

It means that the ratios of the lengths of corresponding sides are equal.

Front

If \( AB \cong DE \) and \( AC \cong DF \), what can we conclude about \( \Delta ABC \) and \( \Delta DEF \)?

Back

We can conclude that \( \Delta ABC \sim \Delta DEF \) if the angles are also congruent.

Front

What is the significance of the AA criterion for similarity?

Back

If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar (AA criterion).

Front

What is the SSS similarity criterion?

Back

If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar (SSS criterion).

Front

What is the SAS similarity criterion?

Back

If two sides of one triangle are proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar (SAS criterion).