Triangle Theorems Review

Front

What is the Triangle Sum Theorem?

Back

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.

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

How do you find the missing length in a triangle using proportions?

Back

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

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): a² + b² = c².

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 relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where 1 is the length of the side opposite the 30-degree angle.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Front

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

Back

Two triangles are similar if two angles of one triangle are equal to two angles of another triangle (Angle-Angle criterion).

Front

What is the definition of an altitude in a triangle?

Back

An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side.

Front

What is the definition of a median in a triangle?

Back

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.