4.2 Triangle Inequality Theorems

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, what must be true?

Back

a + b > c, a + c > b, and b + c > a.

Front

What is the relationship between the longest side and the angles in a triangle?

Back

The longest side of a triangle is opposite the largest angle.

Front

How can you determine the smallest side of a triangle given the angles?

Back

The smallest side is opposite the smallest angle.

Front

Given sides 3, 4, and 5, can these lengths form a triangle?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

If one side of a triangle is 10, and the other two sides are 6 and 8, can these lengths form a triangle?

Back

No, because 6 + 8 is not greater than 10.

Front

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

Back

The larger the angle, the longer the side opposite that angle.

Front

If the angles of a triangle are 30°, 60°, and 90°, what can you say about the sides?

Back

The side opposite the 90° angle is the longest, and the sides are in the ratio 1:√3:2.

Front

What is the sum of the angles in any triangle?

Back

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

Front

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

Back

It is an isosceles triangle.