Question

Select all the conditions for which it is possible to construct a triangle.

Group of answer choices


A triangle with angle measures LaTeX: 60^\circ 60 ∘ , LaTeX: 80^\circ 80 ∘ , and LaTeX: 80^\circ 80 ∘


A triangle with side lengths 4 cm, 5 cm, and 6 cm


A triangle with side lengths 4 cm, 5 cm, and 15 cm


A triangle with side lengths 4 cm and 5 cm and a LaTeX: 50^\circ 50 ∘ angle


A triangle with angle measures LaTeX: 30^\circ 30 ∘ and LaTeX: 60^\circ 60 ∘ , and a 3 cm side length

Answer 1

A triangle with side lengths 4 cm, 5 cm, and 6 cm

A triangle with side lengths 4 cm, 5 cm, and 15 cm

A triangle with side lengths 4 cm and 5 cm and a 50∘ angle

A triangle with angle measures 30 ∘ and 60 ∘ , and a 3 cm side length

Explanation:

A triangle measuring 60 ∘, 80∘ and 80∘ is more than sum of angles of a triangle (180∘). This cannot be constructed as triangle because it is more than 180∘.

A triangle can be constructed, If the sum of any two sides is greater than third side,

Thus, a triangle with side lengths 4 cm, 5 cm, and 6 cm can be constructed because;

4 cm + 5cm > 6 cm

A triangle with side lengths 4 cm, 5 cm, and 15 cm can be constructed as well, because;

5 cm + 15 cm > 4 cm

A triangle with side lengths 4 cm and 5 cm and a 50 ∘ angle can be constructed ( two sides and an angle between them)

A triangle with angle measures 30 ∘ and 60 ∘ , and a 3 cm side length can be constructed ( two angles and a side between them)