Mastery Test - Triangle Inequality

The measure of an exterior angle of a triangle is always

• Greater than its adjacent interior angle.

• Less than its adjacent interior angle.

• greater than either remote interior angle.

• less than either remote interior angle.

Sum of any two sides of a triangle is always _______ the third side of the triangle.

• 
  greater than

• equal to

• less than

• None of the above

Which of the following theorems on triangle inequalities states that the measure of an exterior angle of a triangle is greater than the measure of either remote interior angle?

• Triangle Inequality Theorem

• Angle-Side Relationship Theorem

• Exterior Angle Inequality Theorem

• Hinge Theorem or SAS Inequality Theorem

Which of the following angles are remote interior angles to angle d?

• Angle a and Angle b

• Angle b and Angle c

• Angle a and Angle c

• Angle a and Angle b and Angle c

What theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side?

• Triangle Inequality Theorem

• Angle-Side Relationship Theorem

• Exterior Angle Inequality Theorem

• Hinge Theorem or SAS Inequality Theorem

From the given diagram below, if ∠BOQ = 120°, then what are the values of angles x and y?

• 120° & 120°

• 75° & 45°

• 120° & 60°

• 120° & 45°

Two sides of an isosceles triangle measure 3 inches and 7 inches. Which could be the length of the third side?

• 8 inches

• 7 inches

• 5 inches

• 3 inches

Two sides of a triangle have side lengths of 17 meters and 12 meters.  What is the range of possible lengths for the third side?

• 12 < x < 17

• 5 < x < 17

• 12 < x < 29

• 5 < x < 29

It states that “If two sides of a triangle are congruent, then angles opposite those sides are congruent”.

• Converse of Hinge Theorem

• Converse of the Isosceles Triangle Theorem

• Hinge Theorem

• Isosceles Triangle Theorem

It states that “If two angles of a triangle are congruent, then sides opposite those angles are congruent”.

• Converse of Hinge Theorem

• Converse of the Isosceles Triangle Theorem

• Hinge Theorem

• Isosceles Triangle Theorem