Is it possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°
, 50°
, and 100°
? Use the given sides and angles to explain why or why not.
(4 points)
No, it is not possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°, 50°, and 100°.
In an isosceles triangle, two sides have equal lengths. In this case, the given side lengths are 6 cm, 9 cm, and 12 cm. Since it is stated that the triangle is isosceles, two of the side lengths must be equal. However, none of the given side lengths are equal to each other.
Furthermore, the sum of the angles in any triangle must be 180°. In this case, the given angles are 30°, 50°, and 100°, which add up to 180°. However, in an isosceles triangle, the base angles (the angles opposite the equal sides) are equal. Since the angles given are not equal, it is not possible for this triangle to be isosceles.
Therefore, it is not possible to draw an acute isosceles triangle with the given side lengths and angles.