Mathematics 8 Quarterly Exam

Triangle ABC has side lengths AB = 6, BC = 8, and AC = 12. Which theorem can be used to determine if triangle ABC is a valid triangle?

• Hinge Theorem

• Triangle Inequality Theorem

• Linear Pair Theorem

• Exterior Angle Inequality Theorem

What is the other term used for SAS Inequality Theorem?

• Hinge Theorem

• Converse of Hinge Theorem

• Triangle Inequality Theorem

• Exterior Angle Inequality Theorem

Which of the following statements is correct based on the Triangle Inequality Theorem when examining a triangle with side lengths of 4 cm, 6 cm, and 9 cm?

• The triangle is valid regardless of the lengths of its sides.

• The triangle is not valid since 4 + 6 = 10, which is equal to 9.

• The triangle is valid since 4 + 6 = 10, which is greater than 9.

• The triangle is not valid since 4 + 6 = 10, which is not greater than 9.

Which of the following sets of side lengths forms a triangle according to the Triangle Inequality Theorem?

• 3 cm, 4 cm, 9 cm

• 6 cm, 7 cm, 13 cm

• 9 cm, 11cm, 20cm

• 10 cm, 11 cm, 20 cm

For a triangle to be possible, which of the following conditions must be satisfied according to the Exterior Angle Inequality Theorem?

• The measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle.

• The measure of an exterior angle is greater than the sum of the measures of the two opposite(remote) interior angles of the triangle.

• The measure of an exterior angle is greater than the difference between the measures of the two opposite(remote) interior angles of the triangle.

• The measure of an exterior angle is equal to the difference between the measures of the two opposite(remote) interior angles of the triangle.

Consider a triangle with interior angles measuring 30º, 50º, and 100º. What is the measure of the corresponding exterior angle to the angle measuring 50⁰?

• 30º

• 50º

• 80º

• 130º

Using the Triangle Inequality Theorem, determine the possible range of values for x when the side lengths of a triangle are given as x, 9, and 12.

• 9 < x < 12

• 12 < x < 9

• 3 < x < 21

• 21 < x < 3

Consider a triangle with side lengths of 10 cm, 14 cm, and 26 cm. Which of the following statements is TRUE according to the Triangle Inequality Theorem?

• The triangle is possible since 10 - 14 > 26.

• The triangle is possible since 10 + 14 > 26.

• The triangle is not possible since 10 - 14 < 26.

• The triangle is not possible since 10 + 14 < 26.

In Figure 2, arrange the angles from smallest to largest.

• ∠A, ∠B, ∠C

• ∠A, ∠C, ∠B

• ∠B, ∠A, ∠C

• ∠C, ∠A, ∠B

Refer to Figure 3. Which is the largest side of the ∆EFG?

• EF

• EG

• FG

• FE