Is it possible to draw an acute isosceles triangle with side lengths of 6 cm, 9 cm, and 12 cm and angles of 30°30°, 50°50°, and 100°100° ? Use the given sides and angles to explain why or why not.

Answer 1

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°.

To understand why, we need to examine the properties of an acute isosceles triangle. An isosceles triangle has two sides of equal length, and in an acute isosceles triangle, all three angles are acute angles (less than 90°).

In this case, the side lengths of 6 cm, 9 cm, and 12 cm tell us that two sides are equal in length. Without loss of generality, let's assume that the side lengths of 6 cm and 9 cm are equal.

However, the given angles of 30°, 50°, and 100° lead to a contradiction. In a triangle, the sum of the three angles is always 180°. Since we have an angle of 100°, the sum of the other two angles must be 180° - 100° = 80°. But the given angles of 30° and 50° add up to 80°, which means that there is no room for a third angle in this triangle.

Therefore, it is not possible to draw an acute isosceles triangle with the given side lengths and angles.

Answer 2

The measures of the angles in an equilateral triangle are equal. What is the measure of each angle of an equilateral triangle? (1 point)

Answer 3

The measure of each angle in an equilateral triangle is 60 degrees.

Answer 4

Which quadrilateral has one pair of parallel sides, but is not a parallelogram? (1 point) Responses

Answer 5

A trapezoid is a quadrilateral that has one pair of parallel sides, but it is not a parallelogram.

Answer 6

The sides of a triangle measure 3 cm, 5 cm, and 7 cm. One of the angles is 120°120° . Which type of triangle is it? (1 point) Responses

Answer 7

The given triangle with side lengths of 3 cm, 5 cm, and 7 cm and an angle of 120° is an obtuse scalene triangle.