Triangle Midsegments & Inequalities

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and its length is half the length of that side.

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

If a triangle has sides of lengths 7 and 10, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 3 and less than 17.

Front

What does it mean for segments to be parallel in a triangle?

Back

Parallel segments in a triangle do not intersect and maintain a constant distance apart. In the context of midsegments, they are equal in length and correspond to the sides of the triangle.

Front

How do you find the length of a midsegment?

Back

To find the length of a midsegment, take half the length of the side of the triangle that it is parallel to.

Front

What is the relationship between the angles formed by a midsegment and the triangle's angles?

Back

The angles formed by a midsegment are equal to the angles of the triangle that are not adjacent to the midsegment.

Front

What is the significance of the midsegment theorem?

Back

The midsegment theorem states that the midsegment of a triangle is parallel to one side of the triangle and its length is half the length of that side.

Front

If a triangle has sides of lengths 5, 12, and x, what is the range of possible values for x?

Back

x must be greater than 7 and less than 17.

Front

What is the measure of an exterior angle of a triangle?

Back

An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Front

How can you determine if a triangle is valid based on its side lengths?

Back

A triangle is valid if the sum of the lengths of any two sides is greater than the length of the third side.