vertical angles
Vertical angles are pairs of non-adjacent angles that are opposite each other when two lines intersect
Vertical angles are pairs of non-adjacent angles that are opposite each other when two lines intersect. These angles are formed by a pair of opposite rays. Vertical angles have equal measures, meaning they are congruent to each other.
To better understand vertical angles, imagine two lines intersecting each other. This intersection creates four angles. The angles that are directly across from each other (opposite rays) are called vertical angles.
Let’s consider the following diagram:
a——-b
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c——-d
In this diagram, line segment ab intersects with line segment cd at point c. Now, we have four angles: angle acb, angle cbd, angle bcd, and angle adc.
Angles acb and bcd are vertical angles because they are opposite each other. Similarly, angles cbd and adc are also vertical angles.
It is important to note that vertical angles do not have to be adjacent. They can be on any side of the intersection. As long as they are opposite angles, they are considered vertical angles.
The main property of vertical angles is that their measures are equal. In other words, angle acb is congruent to angle bcd, and angle cbd is congruent to angle adc.
For example, if angle acb has a measure of 45 degrees, then angle bcd will also have a measure of 45 degrees.
This property can be useful when solving geometry problems or proving theorems. It helps establish relationships between angles and can be used to solve equations involving angles.
In summary, vertical angles are pairs of opposite angles formed when two lines intersect. They have equal measures and are often used in geometric proofs and problem-solving.
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