Honors Geometry: Inequalities in One Triangle

Front

Can a triangle have sides with the given lengths: 4 m, 5 m, 9 m?

Back

No, the sum of the lengths of the two shorter sides (4 m + 5 m = 9 m) must be greater than the length of the longest side (9 m). This is known as the Triangle Inequality Theorem.

Front

Is it possible to construct a triangle with sides 15, 37, 53?

Back

No, the sum of the lengths of the two shorter sides (15 + 37 = 52) must be greater than the length of the longest side (53). This violates the Triangle Inequality Theorem.

Front

Where is the smallest angle located in a triangle?

Back

The smallest angle is located across from the smallest side.

Front

What does the Triangle Inequality Theorem state?

Back

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

Front

If side DE is less than side DG, what can be inferred about the angles opposite these sides?

Back

Angle E is less than angle G, as the side lengths are directly related to the angles opposite them.

Front

Order the sides from greatest to least if side lengths are a = 5, b = 7, c = 3.

Back

b, a, c (7, 5, 3).

Front

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

Back

In a triangle, the larger the angle, the longer the side opposite it.

Front

If a triangle has sides of lengths 8, 15, and 17, is it a right triangle?

Back

Yes, it is a right triangle because it satisfies the Pythagorean theorem: 8^2 + 15^2 = 17^2.

Front

What is the Pythagorean theorem?

Back

Front

What is the definition of an isosceles triangle?

Back

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