DAY 22 CONGRUENCE OF ALTERNATE INTERIOR ANGLES INTRODUCTION

DAY 22 – CONGRUENCE OF ALTERNATE INTERIOR ANGLES

INTRODUCTION So far we have discussed alternate angles and some of their basic properties. They are one of the several types of angles formed when a transversal intersects a pair of parallel lines. One the pair of angles alternate angles. These angles are always congruent. We also categorized them into alternate interior angles and alternate exterior angles. In this lesson, we are going to further our discussion on alternate interior angles by showing that they are congruent.

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Alternate interior angles Two interior angles between two distinct parallel lines located on opposite sides of the transversal line. In the figure above, 1 and 4 are alternate interior angles. Similarly, 2 and 3 are alternate interior angles.

Proving that alternate interior angles are equal We are going to prove that alternate interior angles are equal using two pairs of parallel lines that will intersect forming a parallelogram. Then, we will later use the basic geometrical properties attributed to the parallelogram to show this congruence.

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