Similarity and Geometric Mean

Front

What is the definition of similar triangles?

Back

Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

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, 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 corresponding sides of two triangles are in proportion, 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, the triangles are similar.

Front

What is the geometric mean of two numbers a and b?

Back

Front

If two triangles are similar, how do you find the length of a side in one triangle if you know the corresponding side in the other triangle?

Back

Front

What is the Triangle Proportionality Theorem (TPT)?

Back

The Triangle Proportionality Theorem states that if a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally.

Front

What is the converse of the Triangle Proportionality Theorem (TPT Converse)?

Back

The converse of the Triangle Proportionality Theorem states that if a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Front

How do you determine if two triangles are similar using the SSS~ criterion?

Back

To determine if two triangles are similar using SSS~, check if the ratios of the lengths of corresponding sides are equal.

Front

What is the relationship between the heights of similar triangles?

Back

The heights of similar triangles are in the same ratio as the lengths of their corresponding sides.