summative test

What does the Triangle Inequality Theorem state?

• The sum of the interior angles of a triangle is always 180°

• The square of the hypotenuse is equal to the sum of the squares of the other two sides.

• The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

• The exterior angle of a triangle is equal to the sum of the opposite interior angles.

Which theorem states that an exterior angle of a triangle is greater than either of its opposite interior angles?

• Pythagorean Theorem

• Exterior Angle Inequality Theorem

• Triangle Inequality Theorem

• Hinge Theorem

The Hinge Theorem is also known as which of the following?

• SAS Inequality Theorem

• AAS Inequality Theorem

• ASA Inequality Theorem

• SSS Inequality Theorem

Why does the Triangle Inequality Theorem hold true for all triangles?

• It helps determine the area of the triangle.

• It ensures that triangles always have three sides.

• It guarantees the formation of a closed figure.

• It validates the relationship between side lengths in a triangle.

A triangle has two side lengths of 6 cm and 10 cm. What is the possible length of the third side?

• 3 cm

• 5 cm

• 14 cm

• 16 cm

In a triangle, an exterior angle measures 120° and one of the opposite interior angles is 40°. What is the measure of the other opposite interior angle?

• 40°

• 60°

• 80°

• 100°

Examine the following sets of three side lengths. Which set(s) satisfy the Triangle Inequality Theorem?

• Set A: 9, 11, 15

• Set B: 3, 7, 10

• Set C: 5, 12, 17

• Set D: 2, 3, 6

Compare two triangles: Triangle 1 has side lengths of 5 cm, 7 cm, and 9 cm, while Triangle 2 has side lengths of 6 cm, 8 cm, and 10 cm. Which triangle has a greater angle, and why?

• Triangle 1, because the sides are closer in length.

• Triangle 2, because it follows the Hinge Theorem.

• Triangle 1, because the Triangle Inequality Theorem does not apply.

• Triangle 2, because its largest side forms the largest angle.

What does the Exterior Angle Inequality Theorem state?

• The exterior angle of a triangle is greater than either of its opposite interior angles.

• The sum of the interior angles of a triangle is 180°.

• The longest side of a triangle is opposite the largest angle.

• The smallest angle in a triangle is opposite the smallest side.

If a triangle has two sides measuring 5 cm and 12 cm, what is the range of possible lengths for the third side?

• Greater than 7 cm and less than 17 cm

• Greater than 5 cm and less than 12 cm

• Greater than 7 cm and less than 12 cm

• Greater than 5 cm and less than 17 cm