5.4 - 5.5 REVIEW

Front

What is the length of the midsegment \( \overline{RQ} \) in a triangle with bases of lengths 4 and 12?

Back

The length of the midsegment is the average of the two bases: \( \frac{4 + 12}{2} = 8 \).

Front

Can the sides of a triangle have lengths 3, 9, and 4?

Back

No, because the sum of the lengths of any two sides must be greater than the length of the third side (3 + 4 < 9).

Front

Which of the following would NOT work to make a triangle with the two side lengths of 2 and 6? (Options: 6, 7, 5, 4)

Back

4, because the third side must be less than the sum of the other two sides (2 + 6 > 4) and greater than their difference (6 - 2 < 4).

Front

Can the sides of a triangle have lengths 15, 8, and 17?

Back

Yes, because 15 + 8 > 17, 15 + 17 > 8, and 8 + 17 > 15.

Front

Find the value of x in the equation 2x + 3 = 15.

Back

x = 6.

Front

What is the Triangle Inequality Theorem?

Back

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

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

Yes, because \( 5^2 + 12^2 = 13^2 \) (25 + 144 = 169).

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle and is parallel to the third side.

Front

How do you find the perimeter of a triangle?

Back

The perimeter of a triangle is found by adding the lengths of all three sides.

Front

What is the formula for the area of a triangle?

Back

The area of a triangle is given by \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \).