Practice Task: Proving Inequalities in a Triangle

Which of the following is the correct ascending arrangement of the measures of the angles of ∆CEA?

• ∠𝐸, ∠𝐴, ∠𝐶

• ∠𝐴, ∠𝐶, ∠𝐸

• ∠𝐸, ∠𝐶, ∠𝐴

• cannot be determined

Which statement below defines Addition Property of Equality?

• For all real numbers, 𝑝, 𝑞 and 𝑟, if 𝑝 = 𝑞, then 𝑝 + 𝑟 = 𝑞 + 𝑟.

• For all real numbers, 𝑝, 𝑞 and 𝑟, if 𝑞 = 𝑟, then 𝑝 + 𝑟 = 𝑞 + 𝑟.

• For all real numbers, 𝑝, 𝑞 and 𝑟, if 𝑝 = 𝑞, then 𝑝 + 𝑞 = 𝑞 + 𝑟.

• For all real numbers, 𝑝, 𝑞 and 𝑟, if 𝑝 = 𝑟, then 𝑝 + 𝑟 = 𝑞 + 𝑟.

Which of the following theorems states that “base angles of isosceles triangles are congruent”?

• Linear Pair Theorem

• Vertical Angles Theorem

• Exterior Angle Theorem

• Isosceles Triangle Theorem

What triangle inequality theorem states that “If one side of a triangle is longer than a second side, then the angle opposite the longer side is larger than the angle opposite the second side”?

• Exterior Angle Inequality Theorem

• Triangle Inequality Theorem 1 (Ss→Aa)

• Triangle Inequality Theorem 2 (Aa→Ss)

• Triangle Inequality Theorem 3 (S1 + S2 > S3)

For all real numbers 𝑝, 𝑞 and 𝑟, if 𝑝 = 𝑞 and 𝑞 = 𝑟, then 𝑝 = 𝑟.

• Addition Property of Equality

• Reflexive Property of Equality

• Transitive Property of Equality

• Substitution Property of Equality

What is the answer in number 1?

• 𝑀𝑂 ≅ 𝑂𝐸̅

• |𝐸𝑅| + |𝑅𝑂| > |𝑀𝑂|

• |𝐸𝑅| + |𝑅𝑂| > |𝑂𝐸|

• Cannot be determined

What is the answer in number 2?

• MO ≅ OE

• MO ≅ OR

• OR ≅ OE

• Cannot be determined

What is the answer in number 3?

• Hinge Theorem

• Triangle Inequality Theorem 3

• Substitution Property

• Converse of Hinge Theorem

What is the answer in number?

• Hinge Theorem

• Triangle Inequality Theorem 3

• Substitution Property

• Converse of Hinge Theorem

Which theorem below does not belong to the inequality theorems in one triangle?

• Hinge Theorem

• Exterior Angle Inequality Theorem

• Triangle Inequality Theorem 1 (Ss→Aa)

• Triangle Inequality Theorem 2 (Aa→Ss)