G.5 Triangle Inequalities

Front

What is the Triangle Inequality Theorem?

Back

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

Front

If a triangle has sides of lengths a, b, and c, how can you determine the longest side?

Back

The longest side can be determined by comparing the lengths of the sides. The side opposite the largest angle is the longest.

Front

Given sides of a triangle: 5, 7, and x, what is the range of possible values for x?

Back

According to the Triangle Inequality Theorem, x must satisfy: |5 - 7| < x < 5 + 7, which simplifies to 2 < x < 12.

Front

What is a median in a triangle?

Back

A median is a line segment from a vertex to the midpoint of the opposite side, dividing the triangle into two smaller triangles of equal area.

Front

How do you find the length of a median given the lengths of the sides of a triangle?

Back

Front

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

Back

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

Front

How do you order the sides of a triangle from least to greatest?

Back

To order the sides, compare their lengths directly. The side with the smallest length is first, followed by the next smallest, and so on.

Front

What is the significance of the median in triangle problems?

Back

Medians are significant because they help in finding the center of mass of the triangle and can be used to solve various geometric problems.

Front

If two sides of a triangle are equal, what type of triangle is it?

Back

It is an isosceles triangle.

Front

What is the sum of the angles in any triangle?

Back

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