Question

Draw a picture and label the necessary parts in order to verify that the sum of the angles of any triangle is 180 degrees.

Answer 1

To verify that the sum of the angles in a triangle is 180 degrees, draw a triangle, extend a base to form a straight line, and draw a parallel line through the opposite vertex. Label the alternate interior angles and sum them to see that they add up to 180 degrees, using a ruler and protractor for precision.

Step-by-step explanation:

To verify that the sum of the angles in any triangle equals 180 degrees, you can follow these steps:

1. Draw a triangle and label the three angles A, B, and C.
2. Extend one side of the triangle to form a straight line.
3. Draw a line parallel to the base of the triangle that passes through the vertex opposite the base.
4. Label the angles formed by the parallel lines and transversal with the corresponding angles in the triangle, noting that they are equal due to the Alternate Interior Angles Theorem.
5. The sum of the angles on a straight line is 180 degrees, and since the alternate interior angles are equal to the angles in the triangle, the sum of angles A + B + C must also be 180 degrees.

Using a ruler and protractor, you can measure each angle within the triangle and verify that their sum is indeed 180 degrees. This visual method demonstrates why any three sided figure lying on a plane must have angles adding up to 180 degrees. This concept is fundamental in geometry and is an important property of triangles.