vertical angles are congruent
Vertical angles are a type of pair of angles formed by two intersecting lines
Vertical angles are a type of pair of angles formed by two intersecting lines. When two lines intersect each other, they create four angles at the point of intersection. Among these four angles, the pairs of angles that are opposite each other and do not share a common side are known as vertical angles.
The key property of vertical angles is that they are congruent, which means they have the same measure. This property holds true regardless of the angles’ size or shape. In other words, if two lines intersect and form a pair of vertical angles, those angles will always be equal to each other.
To further explain this idea, let’s consider an example. Suppose we have two intersecting lines, line AB and line CD. At the point where these lines intersect, four angles are formed: angle 1, angle 2, angle 3, and angle 4.
A C
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B–/–D
In this case, angle 1 and angle 3 are vertical angles, as they are opposite each other and do not share a side. Similarly, angle 2 and angle 4 are vertical angles.
Now, according to the property of vertical angles, angle 1 and angle 3 will have the same measure. This can be represented mathematically as:
Angle 1 = Angle 3
Similarly, angle 2 and angle 4 will also have the same measure:
Angle 2 = Angle 4
This property holds true for any pair of vertical angles formed by intersecting lines.
Understanding the concept of vertical angles being congruent is important in solving various mathematical problems involving angles, such as proving the congruence of triangles or finding unknown angles in geometric figures.
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