show that the measure of each angle of an equilateral triangle is 60 degree
All of the angles of an equilateral triangle are the same.
180 / 3 = 60
To show that the measure of each angle of an equilateral triangle is 60 degrees, we can use the fact that the sum of the angles in any triangle is always 180 degrees.
Step 1: Start by drawing an equilateral triangle.
Step 2: Label the three angles of the equilateral triangle as A, B, and C.
Step 3: Since all sides of the equilateral triangle are equal, let's label the length of each side as "s".
Step 4: Draw a line segment from the vertex of angle A to the midpoint of the opposite side.
Step 5: This line segment divides the equilateral triangle into two congruent right triangles.
Step 6: Since the opposite sides of a right triangle are equal in length, the two right triangles created are congruent.
Step 7: By the properties of congruent triangles, we can conclude that the angles in the two right triangles are also congruent.
Step 8: Let's focus on one of the right triangles. The right angle is 90 degrees.
Step 9: Since the two congruent angles in a right triangle must add up to 90 degrees, the remaining angle in each right triangle is (180 - 90)/2 = 45 degrees.
Step 10: Since the right triangles are congruent, the remaining angle in each of the two congruent right triangles is 45 degrees.
Step 11: By the properties of angles in a triangle, the sum of the angles in the equilateral triangle is 180 degrees.
Step 12: Therefore, if we let angle A be 60 degrees, then the sum of angles A, B, and C will be 60 + 60 + 60 = 180 degrees.
Step 13: Hence, we have shown that the measure of each angle of an equilateral triangle is 60 degrees.