Proving Similar Triangles

Front

What is the AA similarity theorem?

Back

The AA (Angle-Angle) similarity theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Front

What is the SSS similarity theorem?

Back

The SSS (Side-Side-Side) similarity theorem states that if the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the SAS similarity theorem?

Back

The SAS (Side-Angle-Side) similarity theorem states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are congruent, then the triangles are similar.

Front

How can you determine if two triangles are similar?

Back

You can determine if two triangles are similar by using the AA, SSS, or SAS similarity theorems.

Front

What does it mean for triangles to be similar?

Back

Triangles are similar if they have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are in proportion.

Front

If two triangles have two pairs of equal angles, what can be concluded?

Back

If two triangles have two pairs of equal angles, they are similar by the AA similarity theorem.

Front

If the sides of triangle A are 3, 4, 5 and the sides of triangle B are 6, 8, 10, are they similar?

Back

Yes, triangle A and triangle B are similar by the SSS similarity theorem because the sides are in proportion (1:2).

Front

What is the relationship between similar triangles and their areas?

Back

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

Front

Can two triangles be similar if one is a right triangle and the other is not?

Back

Yes, two triangles can be similar regardless of whether one is a right triangle and the other is not, as long as their corresponding angles are equal.

Front

What is the significance of the included angle in the SAS similarity theorem?

Back

The included angle in the SAS similarity theorem must be congruent for the triangles to be considered similar.