Geometry is a significant subject of mathematics concerned with the study of various shapes. It serves as an introduction to the analysis of lines and angles. A straight line is defined as a line devoid of curves and as the shortest distance between two locations. When a line segment intersects at a point, an angle is generated.
The term “supplementary angles” refers to those that add up to 180 degrees. For instance, angles 130° and 50° are supplementary angles since the total of their values equals 180°. Complementary angles, likewise, add up to 90 degrees. When the two supplementary angles are united, a straight line and a straight angle are formed.
However, it should be emphasized that the two supplementary angles do not have to be adjacent. Thus, any two angles may be considered supplementary if their total equals 180°.
Significant features or properties of supplementary angles include the following:
- When the two angles sum up to 180°, they are considered to be supplementary angles.
- Two angles together form a straight line, although the angles do not have to be adjacent.
- In additional angles, the letter “S” denotes the “Straight” line. This implies they make a 180-degree angle.
Supplementary angles are classified into two types:
Complementary angles adjacent
Supplementary angles that are not contiguous
- Adjacent Additional angles:
Adjacent supplementary angles are those that share an arm and a vertex. The same line segment and vertex connect adjacent supplementary angles.
- Supplementary angles that are not adjacent:
Non-adjacent supplementary angles are those that lack a common arm and vertex. The additional angles that are not contiguous do not share a line segment or vertex.
Corresponding Angles:
Corresponding angles are those created when two parallel lines are crossed by another line (i.e. the transversal). For instance, in the image below, angles p and w are comparable angles.
Examples and Types of Corresponding Angles
Any angle created on the other side of the transversal is an example of a relative angle. Now, it’s worth noting that the transversal may cross two parallel or two non-parallel lines.
Thus, related angles may be classified into two categories:
Parallel lines and transversals create corresponding angles.
Angles produced by non-parallel lines and transversals that correspond
You must have learnt about the many kinds of lines and angles in mathematics. Only equivalent angles created by the intersection of two lines by a transversal will be discussed in this section. Two parallel or non-parallel lines are possible. Therefore, let us study the equivalent angles for both scenarios.
- The postulate of Corresponding Angles:
The equivalent angle postulate asserts that if the transversal meets two parallel lines, the corresponding angles are congruent. In other words, if a transversal meets two parallel lines, the angles formed by the intersection are always equal.
- Triangles with Corresponding Angles:
Corresponding angles in a triangle are those that are contained inside a pair of comparable (or congruent) triangles by a congruent pair of sides. Angles next to one another in a triangle have the same measure.
- A theorem of Corresponding Angles:
According to the corresponding angles theorem statement, “when a line meets two parallel lines, the corresponding angles in the two intersection zones are congruent.”
Notable Points Regarding Corresponding Angles:
- When two parallel lines cross with a third, the angles that have the same relative position at each junction are referred to as comparable angles.
- The related angles are complementary in nature.
- When the matching angles in the two intersection zones are congruent, the two lines are naturally parallel.
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