Math 8 Triangle Inequalities and Probability

Which theorem states that if one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side?

• Triangle Inequality Theorem

• Angle-Side Relationship Theorem

• Exterior Angle Inequality Theorem

• Hinge Theorem or SAS Inequality Theorem

In Triangle Inequality Theorem, which of the following describes the relationship of the sum of its two sides to its third length?

• greater than

• greater than or equal to

• less than

• less than or equal to

Which of the following theorems deals with the two triangles whose two corresponding sides are congruent and whose included angle are unequal?

• SAS Inequality Theorem

• Angle-Side Relationship Theorem

• SSS Inequality Theorem

• Exterior Angle Inequality Theorem

Which of the following could NOT be used as the length of the sides of a triangle?

• 3, 3, 3

• 4, 5, 10

• 5, 7, 9

• 10, 20, 20

Given the figure at the right, which of the following angles is an exterior angle of ∆ DER?

• ∠3

• ∠4

• ∠2

• ∠1

In ∆ 𝑁𝐸𝑇, 𝑁𝐸= 14 cm, 𝐸𝑇̅̅̅̅ = 15 cm, 𝑁𝑇̅̅̅̅ = 16 cm. What is the correct order of the angles when arranged from least to greatest?

• ∠E, ∠N, ∠T

• ∠E, ∠T, ∠N

• ∠T, ∠E, ∠N

• ∠T, ∠N, ∠E

Carlos concluded that the longest side in 𝛥𝑀𝐴𝑃 is 𝐴𝑃̅̅̅̅ after finding that the angle opposite to 𝐴𝑃̅̅̅̅ is the largest angle. What theorem did Carlos use to make such conclusion?

• Triangle Inequality Theorem 1 (𝑆𝑠 → 𝐴𝑎)

• Triangle Inequality Theorem 2 (𝐴𝑎 → 𝑆𝑠)

• Hinge Theorem or SAS Triangle Inequality Theorem

• Converse of Hinge Theorem or SSS Triangle Inequality Theorem

What is the largest angle?

• ∠𝐸

• ∠𝑁

• ∠𝑃

• Cannot be determined.

What is the smallest angle?

• ∠𝐸

• ∠𝑁

• ∠𝑃

• Cannot be determined.

Which property of equality is defined by the statement "For all real numbers 𝑝, 𝑝 = 𝑝"?

• Reflexive Property

• Transitive property

• Symmetric Property

• Substitution Property