Unit 5 Lesson 8 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 3, 4, and 5, does it satisfy the Triangle Inequality Theorem?

Back

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

Front

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

Back

The larger the angle, the longer the opposite side. Conversely, the smaller the angle, the shorter the opposite side.

Front

Can a triangle have two sides of equal length and still satisfy the Triangle Inequality Theorem?

Back

Yes, an isosceles triangle can have two sides of equal length and still satisfy the Triangle Inequality Theorem.

Front

What is an example of a set of lengths that cannot form a triangle?

Back

Lengths 1, 2, and 3 cannot form a triangle because 1 + 2 is not greater than 3.

Front

What is the minimum requirement for three lengths to form a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

If one side of a triangle is 10 units long and the other two sides are 6 and 7 units long, can these lengths form a triangle?

Back

No, because 6 + 7 is not greater than 10.

Front

What is the significance of the Triangle Inequality Theorem in real-world applications?

Back

It helps in determining whether three given lengths can form a triangle, which is essential in fields like engineering and architecture.

Front

How can you determine if three lengths can form a triangle using inequalities?

Back

By checking if a + b > c, a + c > b, and b + c > a for sides a, b, and c.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle where one of the angles is greater than 90 degrees.