Vertical Angle
An vertical angle is formed at the point of intersection of two straight lines or rays. The point of intersection is called vertex and the angle is formed in between the two lines which are measured in degrees.when two consecutive lines cross or cut each other.
When two straight lines intersect each other, four angles are formed at the point of intersection. The two pairs of angles that are formed opposite to each other are called vertical angles. The term ‘vertical’ here refers to the vertex where the lines intersect. These angles are also known as vertically opposite angles. The vertical angles are always equal to each other.
Vertical angles are defined as a pair of angles that are opposite to each other when two straight lines intersect at a point. So there are always two pairs of vertical angles formed at the point of intersection. Vertical angles are opposite to each other at the vertex so they are also called vertically opposite angles.
Properties of Vertical Angle
- Vertical angles are equal to each other
- Two pair of vertical angles is formed at the vertex where two straight lines intersect
- Vertical angles can be complementary or supplementary
- Vertical angles are non-adjacent
The important property of vertical angles is that they are equal to each other. This can be explained by example:
Let’s consider two straight lines AB and CD intersect at point O. Then the angles ∠AOC and ∠BOD are vertical angles and ∠AOD and ∠BOC are also vertical angles. Now as per straight angle property, we know ∠AOC + ∠AOD = 180° and also ∠AOD + ∠BOD = 180°. Therefore, it is proved that ∠AOC = ∠BOD. Similarly, using the above theorem we can prove ∠AOD = ∠BOC. So we can conclude that vertical angles are equal to each other.
It is to be noted that vertical angles or vertically opposite angles will be equal to each other only when the intersecting lines are straight lines.
Congruent Angles
When two or more angles are found to be of equal measurement they are called congruent angles. The congruent angles can be of any type like acute, obtuse, interior, or exterior. The length and direction of two lines forming the angles are not relevant in making congruent angles. The only condition for two angles to be congruent is that they should be equal to each other. Congruent angles are the angles with equal measurement in degrees or radians. Let’s learn about this topic in detail from cuemath.com
How are Congruent Angles Formed?
Congruent angles can be formed in various conditions. These are:
- When two lines are intersected by another line called transversal, the two pairs of inner angles that are formed on the opposite sides of the transversal but on the inner side of the lines are called alternate interior angles. If the two lines that are being intersected are parallel to each other, then the alternate interior angles have equal values and are congruent.
- When two parallel lines are intersected by another line called transversal, the two pairs of angles formed on the same side of the transversal but on the opposite side of the lines are congruent.
- When two straight lines intersect at a point, the vertically opposite pair of angles formed are congruent.
- In a rectangle, square, or parallelogram, the angles formed by the diagonal and the two opposite sides are congruent. These angles are also called ‘Z’ angles as they form a Z pattern.
- When a line intersects another line in a perpendicular position, the four angles formed at the point of intersection are all equal to 90 degrees. So these four angles are congruent.
- Interior angles of a regular polygon are all equal so they are congruent.
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Difference between Vertical Angle and Congruent angles.
When two lines cross each other, they result in two angles opposite A+C and B +. Another way to describe opposing angles is called vertical angles. Vertical angles are harmonious, which means they are both equal.
Based on this theorem of vertical angles, regardless of how you throw your skewers or pencils in a manner that they intersect or how two lines intersect, horizontal angles will always be identical or congruent to each other. This is described as an encapsulation of The Vertical Angles Theorem.
Examples of Vertical angles and Congruent angles
Vertical angles can describe as angles added to are formed when lines meet perpendicularly.
For instance, both W and Y are vertical angles that are other angles. Similar to Z and X Both are vertical angles , which are added angles.
How can you determine Vertical Angles?
There’s no formula that can be used to calculate the vertical angles. It is, however, possible to determine angles that are not well-known by connecting angles as that is illustrated in the following instances.
For instance,
Calculate angles that aren’t known in the figure below.
Explanation
Both 470 and B are horizontal angles. Also, B could be an angle in the range of 447 (vertical angles are equal or equivalent or).
The number 470 and the A are the two angles added. So 1800 = 700
=a = 1330
Two angles constitute vertical angles. Therefore, the sum of c equals 1330.
Example of congruent angle
A congruent angle has the same amount of angle. As an example, the pentagon is composed of five sides, and five angles. Each angle define as having an angle of 108 degrees. Whatever dimension or size that a normal polygon measure with the angles, they are in a congruous expression.
For instance, when two triangles share the same shape as each other, their angles will be the same. This means angles at the same location have the same angle.
Final words
In this article we discussed vertical angles and congruent angles and also we know the difference between them and to know examples of both vertical and congruent angles.
To learn more about the math concept in a detailed manner then visit Cuemath to book a free session.
