Question

1. in an equilateral triangle, all side - lengths are equal and all angle measures are equal. sketch an equilateral triangle. what are the measures of its angles? 2. in an isosceles triangle, which is not equilateral, two side - lengths are equal and two angle measures are equal. sketch three different isosceles triangles. 3. list two different possibilities for the angle measures of an isosceles triangle.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Solve for angles of equilateral triangle

In an equilateral triangle, all angles are equal. Let the measure of each angle be $x$. Then $x + x+x=180^{\circ}$, or $3x = 180^{\circ}$. Solving for $x$, we get $x=\frac{180^{\circ}}{3}=60^{\circ}$.

Step3: Sketch isosceles triangles

For an isosceles triangle (non - equilateral), draw triangles with two equal - length sides. For example, one with two sides of length 5 cm and a base of length 3 cm, another with two sides of length 4 cm and a base of length 6 cm, and a third with two sides of length 7 cm and a base of length 2 cm. The equal - angle pairs are opposite the equal - length sides.

Step4: Find angle measures for isosceles triangles

Possibility 1: Let the equal angles be 40° each. Then the third angle is $180-(40 + 40)=100^{\circ}$.
Possibility 2: Let the equal angles be 70° each. Then the third angle is $180-(70 + 70)=40^{\circ}$.

Answer:

1. Each angle of an equilateral triangle measures 60°.
2. (Sketch three non - congruent isosceles triangles with two equal side lengths and two equal angle measures).
3. Possibility 1: 40°, 40°, 100°; Possibility 2: 70°, 70°, 40°