Geometry Chapter 7: Similarity

Front

What does AA~ stand for in triangle similarity?

Back

AA~ stands for Angle-Angle similarity, which states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What does SAS~ stand for in triangle similarity?

Back

SAS~ stands for Side-Angle-Side similarity, which states that if two sides of one triangle are in proportion to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What does SSS~ stand for in triangle similarity?

Back

SSS~ stands for Side-Side-Side similarity, which states that if the three sides of one triangle are in proportion to the three sides of another triangle, then the triangles are similar.

Front

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

Back

The triangles are similar by the AA~ criterion.

Front

If the sides of triangle A are 4, 6, and 8, and the sides of triangle B are 2, 3, and 4, are the triangles similar?

Back

Yes, the triangles are similar because the sides are in proportion (4:2, 6:3, 8:4).

Front

How can you determine if two triangles are similar using the SAS~ criterion?

Back

To use the SAS~ criterion, check if two sides of one triangle are proportional to two sides of another triangle and if the included angles are equal.

Front

What is the relationship between similar triangles and their corresponding sides?

Back

In similar triangles, the lengths of corresponding sides are in proportion.

Front

If triangle A has sides of lengths 5, 10, and 15, and triangle B has sides of lengths 2.5, 5, and 7.5, are the triangles similar?

Back

Yes, the triangles are similar because the sides are in proportion (5:2.5, 10:5, 15:7.5).

Front

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

Back

The AA~ criterion is significant because it is sufficient to prove that two triangles are similar if two angles are equal.

Front

If triangle A has angles of 30°, 60°, and 90°, what are the angles of a similar triangle?

Back

The angles of a similar triangle will also be 30°, 60°, and 90°.