Sasha says that she drew an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100°. Danielle says that is not possible. Explain, using sides and angles, who is correct.
(4 points)
Danielle is correct.
In an isosceles triangle, two sides are congruent. Therefore, if the side lengths are 6 cm, 9 cm, and 12 cm, it cannot be an isosceles triangle because all sides are different lengths.
Additionally, in an acute triangle, all angles are less than 90 degrees. However, in this case, one of the angles is 100 degrees, which is greater than 90 degrees. Therefore, it cannot be an acute triangle.