Honors Geometry: Inequalities in One Triangle

Front

What is the Triangle Inequality Theorem?

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

Can a triangle have sides with lengths 15 cm, 1 cm, and 15 cm?

Back

Yes, this triangle satisfies the Triangle Inequality Theorem.

Front

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

Back

In a triangle, the largest angle is opposite the longest side, and the smallest angle is opposite the shortest side.

Front

If a triangle has angles measuring 20°, 120°, and 40°, which side is the longest?

Back

The side opposite the 120° angle is the longest.

Front

How do you determine the order of sides in a triangle based on angle measures?

Back

List the sides in order from shortest to longest based on the angles: smallest angle = shortest side, largest angle = longest side.

Front

What is the smallest angle in a triangle with sides 5 cm, 7 cm, and 10 cm?

Back

The smallest angle is opposite the 5 cm side.

Front

How do you list the sides of triangle ΔDEF with angles m∡D = 20°, m∡E = 120°, and m∡F = 40° from shortest to longest?

Back

The sides in order from shortest to longest are EF, DE, DF.

Front

What is the definition of an obtuse triangle?

Back

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

Front

What is the definition of an acute triangle?

Back

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

Front

What is the definition of a right triangle?

Back

A right triangle is a triangle that has one angle measuring exactly 90°.