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.
Danielle is correct. An acute isosceles triangle is a triangle with two sides that are equal in length and two acute angles that are equal in measure. In Sasha's statement, the side lengths given are 6 cm, 9 cm, and 12 cm. Since two sides need to be equal for an isosceles triangle, it is not possible for an isosceles triangle to have side lengths of 6 cm, 9 cm, and 12 cm.
Additionally, the angles given in Sasha's statement are 30°, 50°, and 100°. In an acute triangle, all three angles need to be less than 90°. However, the angle measures of 30°, 50°, and 100° do not satisfy this condition. Thus, Sasha's statement contradicts the properties of an acute isosceles triangle.