Unit 5 Test

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Front

What is the range of possible lengths for the third side of a triangle with sides of lengths 12 and 7?

Back

5 < x < 19, where x is the length of the third side.

Front

True or False: A triangle can have side lengths of 8, 9, and 15.

Back

True, because the sum of the lengths of any two sides (8 + 9 = 17) is greater than the length of the third side (15).

Front

How do you find the length of a side in a triangle when given the lengths of the other two sides?

Back

Use the Triangle Inequality Theorem to determine the possible lengths of the unknown side.

Front

What is a centroid in a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it is also the center of mass of the triangle.

Front

If a triangle has sides of lengths 6, 8, and 10, is it a right triangle?

Back

Yes, because it satisfies the Pythagorean theorem: 6² + 8² = 10².

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

What is the significance of the centroid in triangle CDF?

Back

The centroid divides each median into a ratio of 2:1, with the longer segment being closer to the vertex.

Front

How do you determine if a set of three lengths can form a triangle?

Back

Check if the sum of the lengths of any two sides is greater than the length of the third side.

Front

What is the maximum possible length of the third side of a triangle with sides measuring 12 and 7?

Back

The maximum possible length is less than the sum of the two sides, which is 19.