Similarity in Right Triangles

Front

What is the definition of similar triangles?

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is the Side-Angle-Side (SAS) similarity criterion?

Back

The SAS similarity criterion states that if one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in proportion, then the triangles are similar.

Front

What is the Angle-Angle (AA) similarity criterion?

Back

The AA similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the relationship between the sides of similar triangles?

Back

The corresponding sides of similar triangles are proportional, meaning the ratios of the lengths of corresponding sides are equal.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, AC = 6, and DE = 8, what is the length of DF?

Back

DF = 12. Since the triangles are similar, the ratio of the sides AB/DE = AC/DF = 4/8 = 6/DF. Solving gives DF = 12.

Front

How do you find the length of a side in similar triangles?

Back

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

Front

What is the definition of a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): c² = a² + b².

Front

If two right triangles are similar, how do their hypotenuses compare?

Back

If two right triangles are similar, the lengths of their hypotenuses are in the same ratio as the lengths of their corresponding sides.

Front

What is the definition of a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where their ratio remains constant.