Triangle Midsegment and Triangle Inequality Theorem

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 does the Triangle Inequality Theorem state?

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 4 and 12, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 8 and less than 16.

Front

Order the sides of a triangle with lengths 5, 7, and 10 from least to greatest.

Back

5, 7, 10.

Front

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

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

If one side of a triangle is 10 and another is 6, what is the maximum possible length of the third side?

Back

The maximum possible length of the third side is less than 16.

Front

What is the minimum length of the third side if two sides of a triangle are 8 and 5?

Back

The minimum length of the third side must be greater than 3.

Front

How do you find the length of a midsegment in a triangle?

Back

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

Front

What is the significance of the midsegment in triangle similarity?

Back

The midsegment creates a smaller triangle that is similar to the original triangle.

Front

If a triangle has angles measuring 30°, 60°, and 90°, what is the relationship between the sides?

Back

The side opposite the 30° angle is half the length of the hypotenuse, and the side opposite the 60° angle is √3/2 times the hypotenuse.