Understanding Vertical Angles and Their Congruency | Exploring the Vertical Angles Theorem and Angle Measurements

vertical angles are congruent

Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines

Vertical angles are a pair of non-adjacent angles formed by the intersection of two lines. These angles share a common vertex and are opposite each other. The key property of vertical angles is that they are congruent, which means they have the same measure.

To prove that vertical angles are congruent, we can use the Vertical Angles Theorem. This theorem states that if two lines intersect, then the vertical angles formed are congruent.

Let’s consider two lines, line AB and line CD, intersecting at point E. This intersection creates four angles: ∠AEC, ∠CED, ∠DEB, and ∠BEA. Here, ∠AEC and ∠CED are vertical angles, as well as ∠DEB and ∠BEA.

To prove that the vertical angles are congruent, we need to show that ∠AEC and ∠CED have the same measure. Similarly, ∠DEB and ∠BEA also need to have the same measure.

We can do this by using the properties of parallel lines, alternate interior angles, and corresponding angles. By drawing a transversal line, we can create alternate interior angles ∠CED and ∠DEB. Since alternate interior angles are congruent, we can conclude that ∠CED and ∠DEB have the same measure.

Similarly, using the same transversal line, we can create corresponding angles ∠AEC and ∠BEA. Corresponding angles are congruent, so we can conclude that ∠AEC and ∠BEA also have the same measure.

Therefore, based on the Vertical Angles Theorem and the properties of lines and angles, we can state that vertical angles are congruent.

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