Geometry Triangle Inequality Theorem

The shortest side of a triangle is opposite the smallest angle.

• triangle inequality theorem

• isosceles triangle theorem

• equilateral triangle theorem

• Theoretical triangle theorem

Using the Triangle Inequality Theorem, find the inequality that represents the possible side lengths of the given triangle.

(Note: The triangle is not necessarily drawn to scale)

Which of the following inequalities can be used to prove using the "triangle inequality theorem" that a triangle with sides of lengths 13, 30, and 14 cannot be made?

• 14+30+13>0

• 13+30>14

• 13+14<30

• 14+30>13

Find m∠C in the given figure.

Are the two given triangles shown congruent?

(Note: the triangles are not drawn to scale)

• No, they are not congruent

• Maybe, but there is not enough information to determine

• Yes, they are congruent

What theorem states that in any triangle if you take any 2 sides of the triangle, their sum must be greater than the length of the 3rd side?

• Triangle Inequality Theorem

• Corollary to the triangle exterior angle theorem

• Triangle exterior angle theorem

• SAS inequality theorem

Which is the converse of the hinge theorem

• If 2 sides of one triangle are congruent to 2 sides of another triangle and the included angle (angle between the 2 sides) of the 1st triangle is larger than the included angle of the 2nd triangle, then the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle.

• If 2 sides of a triangle are congruent to 2 sides of another triangle and the 3rd side of the 1st triangle is longer than the 3rd side of the 2nd triangle, then the included angle in the 1st triangle is greater than the included angle in the 2nd triangle.

• 5,6,9 city blocks

• 6,8,14 city blocks

• 7,9,10 city blocks

• 8,15,17 city blocks

• 3.1 cm

• 3.2 cm

• 4.2 cm

• 6.1 cm

• The triangle is obtuse.

• The triangle is scalene.

• The smallest side measures 61 inches.

• The longest side measures 59 inches.

• The triangle RIO is dilated by a scale factor of 1/3, then the perimeter of the dilated triangle will be 3 units smaller.