Geometry 2.3.1 Triangle Inequality Theorem

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

How do you identify the smallest angle in a triangle?

Back

The smallest angle in a triangle is opposite the shortest side.

Front

What is the range of possible lengths for the third side of a triangle given two sides of lengths a and b?

Back

The length of the third side must be greater than the absolute difference of a and b and less than the sum of a and b.

Front

Can the side lengths 4 cm, 7 cm, and 10 cm form a triangle?

Back

Yes, because 4 + 7 > 10, 4 + 10 > 7, and 7 + 10 > 4.

Front

What is the longest side in a triangle?

Back

The longest side is the side opposite the largest angle.

Front

Can the sides of a triangle have lengths 3, 4, and 9?

Back

No, because 3 + 4 is not greater than 9.

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 determine if three lengths can form a triangle?

Back

Use the Triangle Inequality Theorem: check if the sum of any two sides is greater than the third side.

Front

What is the significance of the Triangle Inequality Theorem in geometry?

Back

It helps to determine the feasibility of forming a triangle with given side lengths.

Front

If two sides of a triangle measure 8 and 15, what is the range for the third side?

Back

The third side must be greater than 7 and less than 23.