When two lines cross, the opposing angles created as a result of the junction are known as vertical angles or vertically opposite angles. A pair of vertically opposite angles are always equal to one another. A vertical angle and its neighboring angle are also supplementary angles, which means that they sum up to 180 degrees. For instance, if two lines connect and form an angle, say X = 45°, then the opposite angle is likewise 45°. And the neighboring angle to angle X will be 180 – 45 = 135°.
Intersecting lines are formed when two lines meet at a location in a plane. Parallel lines are those that do not intersect at any point in a plane.
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What are Vertical Angles?
Four angles are generated when two lines intersect. There are two nonadjacent angle pairings. These are known as vertical angles.
Vertical Angles Definition
A pair of nonadjacent angles created by the intersection of two straight lines is referred to as a vertical angle. Vertical angles are positioned across from each other in the corners of the “X” created by two straight lines. Because they are opposite each other, they are also known as vertically opposite angles.
Vertical Angles Theorem
The vertical angles theorem, also known as the vertically opposed angles theorem, says that two opposite vertical angles created when two lines join are always identical (congruent). Let’s take a closer look at the vertical angles theorem and its proof.
Statement: Vertical angles (the opposing angles created when two lines connect) are congruent.
Are Vertical Angles Congruent?
Yes, according to the vertical angle theorem, no matter how you cross your skewers or pencils, or how two crossing lines cross, vertical angles are always congruent, or equal to each other. The Vertical Angles Theorem entrenched this in mathematics.
Are Vertical Angles Adjacent?
Vertical angles, by definition, cannot be adjacent (next to each other). Because opposing angles are vertical, another pair of vertical angles interrupts. Adjacent angles are formed by taking one angle from one pair of vertical angles and another angle from the opposite pair of vertical angles.
Angles of identical measure are called congruent angles. As a result, any angles of equal measure are referred to as congruent angles. They may be found in equilateral triangles, isosceles triangles, and where a transversal connects two parallel lines.
Congruent Angles Definition
Congruent angles are defined in mathematics as “angles of equal measure.” Equal angles, in other words, are congruent angles. If we wish to express that A is congruent to X, we will write it as A X. Consider the following example of congruent angles.
Congruent Angles Theorem
Many theorems are based on congruent angles. We may simply determine if two angles are congruent or not by using the congruent angles theorem. These theorems are as follows:
- Vertical angles theorem
- Corresponding angles theorem
- Alternate angles theorem
- Congruent supplements theorem
- Congruent complements theorem
Drawing Congruent Angles
Using a drawing compass, a straightedge, and a pencil, you may draw congruent angles or compare possibly existing congruent angles.
- Drawing two parallel lines sliced by a transversal is one of the simplest ways to create congruent angles. The appropriate angles in your drawing will be congruent. There will be several pairings of angles that are congruent.
- A right angle or a right triangle is another simple technique to draw congruent angles. Then, using an angle bisector, cut that right angle. If you precisely bisect the angle, you will be left with two congruent sharp angles, each measuring 45°.