Proving Triangles 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 equal, then the triangles are similar.

Front

What is the AA~ similarity criterion?

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

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

Back

SSS~ stands for Side-Side-Side similarity, which states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

Front

What is a similarity statement in geometry?

Back

A similarity statement is a statement that indicates that two geometric figures are similar, often written in the form of ΔABC ~ ΔDEF, meaning triangle ABC is similar to triangle DEF.

Front

What is the significance of the symbol '~' in triangle similarity?

Back

The symbol '~' indicates that two triangles are similar, meaning they have the same shape but may differ in size.

Front

What is the relationship between corresponding angles in similar triangles?

Back

In similar triangles, corresponding angles are equal.

Front

What is the relationship between corresponding sides in similar triangles?

Back

In similar triangles, the lengths of corresponding sides are proportional.

Front

If ΔMNP ~ ΔRST and the length of MN is 12 and RS is 8, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 12:8, which simplifies to 3:2.

Front

How do you find the value of a variable in similar triangles?

Back

To find the value of a variable in similar triangles, set up a proportion using the lengths of corresponding sides and solve for the variable.

Front

What does it mean if two triangles are not similar?

Back

If two triangles are not similar, it means they do not have the same shape, which can be due to differences in angle measures or side lengths.