Honors Geometry 4.7 Triangle Inequalities Progress Check

Front

What does the Hinge Theorem state?

Back

The Hinge Theorem states that if two triangles have two sides of equal length, the triangle with the larger included angle will have a longer third side.

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

Can a triangle be formed with side lengths 10, 12, and 22?

Back

No, because 10 + 12 is not greater than 22.

Front

If two sides of a triangle are 17 meters and 12 meters, what is the range of possible lengths for the third side?

Back

5 < x < 29.

Front

How do you compare the lengths of two sides in a triangle?

Back

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

Front

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

Back

In a triangle, larger angles are opposite longer sides.

Front

Order the sides from least to greatest: DE, VE, DV.

Back

DE, VE, DV.

Front

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

Back

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

Front

What is the significance of the Triangle Inequality Theorem in triangle construction?

Back

It ensures that the lengths of the sides can actually form a triangle.

Front

If QT < ST, what can we infer about the angles opposite these sides?

Back

Angle opposite QT is less than the angle opposite ST.