Question

Which conditions allow the construction of a triangle?

a) A triangle with angle measures 60, 80, and 80 degrees
b) A triangle with side lengths 4cm, 5cm, and 6cm
c) A triangle with side lengths 4cm, 5cm, and 15cm
d) A triangle with side lengths 4cm, 5cm, and a 50-degree angle

Answer 1

To construct a triangle, the sum of the angles must be 180 degrees and the lengths of two sides must be greater than the length of the third side.

Step-by-step explanation:

A triangle can be constructed if the sum of the three angles is 180 degrees and if the length of any two sides is greater than the length of the third side.

1. a) In this case, the sum of the angles is 60 + 80 + 80 = 220 degrees, which is greater than 180, so this does not form a triangle.
2. b) Here, the lengths of the sides are 4cm, 5cm, and 6cm. The sum of any two sides is greater than the third side (4 + 5 > 6, 4 + 6 > 5, 5 + 6 > 4), so this does form a triangle.
3. c) In this case, the lengths of the sides are 4cm, 5cm, and 15cm. The sum of the two smaller sides is not greater than the length of the longest side (4 + 5 = 9 < 15), so this does not form a triangle.
4. d) Here, the lengths of the sides are 4cm, 5cm, and a 50-degree angle. Since we cannot determine the length of the third side based on these given measurements, we cannot confirm if it forms a triangle or not.