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

If a triangle has sides of lengths 4 m, 5 m, and 9 m, can it exist?

Back

No, because 4 + 5 is not greater than 9.

Front

Where is the smallest angle located in a triangle?

Back

The smallest angle is located across from the smallest side.

Front

List the angles of triangle ΔXYZ with sides XY = 12, YZ = 24, ZX = 30 from smallest to largest.

Back

∡Z, ∡X, ∡Y.

Front

List the sides of triangle in order from smallest to largest: PR, QP, RQ.

Back

ext{The order is: } ar{QP}, ar{PR}, ar{RQ}.

Front

What is the relationship between the lengths of sides DE and DG if DE < DG?

Back

This means that side DE is shorter than side DG.

Front

What can be inferred if one angle of a triangle is larger than another?

Back

The side opposite the larger angle is longer than the side opposite the smaller angle.

Front

If a triangle has sides of lengths 7, 10, and 12, what can be said about the angles?

Back

The angle opposite the side of length 7 is the smallest, and the angle opposite the side of length 12 is the largest.

Front

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

Back

In a triangle, larger angles are opposite longer sides.

Front

If two sides of a triangle are equal, what type of triangle is it?

Back

It is an isosceles triangle.