triangle inequalities and hinge theorem

Front

What is the Hinge Theorem?

Back

The Hinge Theorem states that if two triangles have two pairs of equal sides, the triangle with the larger included angle will have the longer third 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

How do you determine if a triangle is scalene?

Back

A triangle is scalene if all three of its sides are of different lengths.

Front

What defines an isosceles triangle?

Back

An isosceles triangle has at least two sides that are of equal length.

Front

What is an equilateral triangle?

Back

An equilateral triangle is a triangle in which all three sides are of equal length and all three angles are equal to 60 degrees.

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

Front

How can you use the SSS inequality theorem?

Back

The SSS inequality theorem can be used to find the range of possible lengths for the third side of a triangle when the lengths of the other two sides are known.

Front

What is the relationship between angles and sides in a triangle according to the Hinge Theorem?

Back

In the Hinge Theorem, the larger the angle, the longer the opposite side.

Front

If two sides of a triangle are 5 and 7, what is the range of possible lengths for the third side?

Back

The length of the third side must be greater than 2 (5 - 7) and less than 12 (5 + 7), so the range is 2 < x < 12.