Proving The Theorem Of Vertical Angles Congruence Using Geometry Principles.

vertical angles are congruent

2 angles whose sides form 2 pairs of opposites rays

Vertical angles are the pair of angles opposite to each other when two lines intersect. The theorem states that vertical angles are congruent, which means they have the same measure.

This theorem can be proved using the basic principles of geometry. When two lines intersect, they form four angles, two on each side of the intersection point. The angle pairs opposite to each other are called vertical angles.

Now imagine two transversals AB and CD intersecting each other at point E, as shown in the diagram below. The vertical angles formed by this intersection are angle AEC and angle BED. Similarly, the vertically opposite angles are angle AED and angle BEC.

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A
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——E——-
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B

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We can prove that angle AEC and angle BED are congruent by considering the properties of alternate interior angles (opposite angles formed when a transversal intersects two parallel lines).

If AB is parallel to CD, then angles AED and BEC are alternate interior angles and hence congruent. By the same logic, angles AEB and CED are also congruent.

Now, since angles AED and AEC are adjacent angles that add up to a straight line (180 degrees) and angles AED and BEC are congruent, it follows that angles AEC and BED are also congruent.

Therefore, we can conclude that vertical angles are congruent. This theorem has important applications in solving problems involving angles, lines, and triangles.

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