5.6 Inequalities in Two Triangles

Front

What does the Hinge Theorem state?

Back

If two triangles have two sides of one triangle congruent to two sides of another triangle, then the angles opposite the longer sides are larger.

Front

If angle A is greater than angle B, what can we say about the sides opposite these angles?

Back

The side opposite angle A is greater than the side opposite angle B.

Front

In triangle ABC, if AB = 5, AC = 7, and angle A is the largest angle, what can we conclude about BC?

Back

BC must be greater than 5 but less than 12.

Front

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

Back

The larger the angle, the longer the side opposite it.

Front

If angle X is the smallest angle in triangle XYZ, what can we say about side YZ?

Back

Side YZ is the smallest side in triangle XYZ.

Front

Using the Hinge Theorem, if angle 1 is greater than angle 2, what can we conclude about the sides opposite these angles?

Back

The side opposite angle 1 is greater than the side opposite angle 2.

Front

If two triangles have two sides equal and the included angle of one triangle is larger than the included angle of the other, what can we say about the third side?

Back

The third side of the triangle with the larger included angle is longer.

Front

What is the significance of the shortest side in a triangle?

Back

The shortest side is always opposite the smallest angle.

Front

If m∠A = 30° and m∠B = 60°, which side is the longest in triangle ABC?

Back

The side opposite angle B is the longest.

Front

In triangle DEF, if DE < DF, what can we conclude about m∠E and m∠F?

Back

m∠E < m∠F.