4B: Proving Triangles Similar

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 congruent to two angles of another triangle, 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 corresponding sides of two triangles are in proportion, 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 proportional to two sides of another triangle and the included angles are congruent, then the triangles are similar.

Front

What is the criteria for two triangles to be considered not similar?

Back

Two triangles are considered not similar if none of the similarity criteria (AA~, SSS~, SAS~) are satisfied.

Front

What is the Vertical Angles Theorem?

Back

The Vertical Angles Theorem states that when two lines intersect, the opposite (or vertical) angles are congruent.

Front

How can you prove triangles are similar using AA~?

Back

To prove triangles are similar using AA~, show that two angles of one triangle are congruent to two angles of another triangle.

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself, which can be used in proving triangle similarity.

Front

If two triangles have one angle congruent and the sides including that angle are proportional, what similarity criterion applies?

Back

The SAS~ (Side-Angle-Side) similarity criterion applies.

Front

What is the relationship between corresponding angles in similar triangles?

Back

In similar triangles, corresponding angles are congruent.

Front

What is the relationship between corresponding sides in similar triangles?

Back

In similar triangles, corresponding sides are in proportion.