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The two purple angles (at A & B) are alternate interior angles, and so they are equal. The straight angle at A is 180 and is the sum of the green, purple and red angles. But the angles in the triangle are these green, purple and red angles. So the sum of the angles in any triangles is 180.
When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.
Alternate Interior Angles. Author: Andy Talmadge. Topic: Angles. Explore alternate interior angle congruence. You can drag A to change separation of parallels, drag B to change point where transversal meets line, drag C to change direction of parallels.
Alternate Interior Angles theorem states, if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Learn more about this interesting concept of alternate interior angles theorem, proof, and solve a few examples.
Topic: Angles. In the applet below, a TRANSVERSAL intersects 2 PARALLEL LINES. When this happens, there are 2 pairs of ALTERNATE INTERIOR ANGLES that are formed. Interact with the applet below for a few minutes, then answer the questions that immediately follow.
Alternate interior angles are formed when a transversal crosses two parallel or non-parallel lines. One way to help you identify this angle pair is to look closely at the words alternate and interior. Alternate tells you that the angles lie on opposite sides of the transversal.
Alternate interior angles can be used to show similarity for two triangles. Example: Parallel line segments AB and DE are cut by transversals AE and BD which intersect at point C.
