Triangle Midsegments & Inequalities

Front

What is a triangle midsegment?

Back

A triangle 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 two sides of a triangle are 8 and 15, what is the range of possible lengths for the third side?

Back

7 < x < 23.

Front

Can a triangle have sides of lengths 5, 5, and 10?

Back

No, because 5 + 5 is not greater than 10.

Front

What is the relationship between the lengths of the sides of a triangle and its angles?

Back

In a triangle, the larger the side, the larger the opposite angle.

Front

What is the length of a midsegment in a triangle with a base of 10 units?

Back

5 units, since the midsegment is half the length of the base.

Front

If one angle of a triangle is 90 degrees, what type of triangle is it?

Back

It is a right triangle.

Front

What is the maximum length of the third side of a triangle with sides 7 and 10?

Back

The maximum length is 16, since 7 + 10 > x.

Front

What is the minimum length of the third side of a triangle with sides 7 and 10?

Back

The minimum length is 3, since 10 - 7 < x.

Front

What is the sum of the angles in a triangle?

Back

The sum of the angles in a triangle is always 180 degrees.