Any two things are said to be congruent when they show the same measurements, shape and dimensions. The literal meaning of the word congruent is ‘same’ or identical. Hence it is understood that Congruent angles do not need to face the same way. Congruent angles are the ones with exactly equal measurements.
Prior to proceeding towards the concept let’s understand
- ANGLE – When two rays meet or intersect at a point they form an angle. The point where rays intersect is the vertex or angle and the two rays forms the arms of the angle. An angle is a form of geometrical shape that can be represented using three alphabets with the alphabet defining the angle in between.
- CONGRUENT – Congruent means same or equal. According to geometry, the term means that one thing (figure) is identical to the other in terms of both shape and size. It can be any shape or figure like a line segment, angle, any quadrilateral or any 3-D shape etc. Whatever the figure may be their corresponding angle are identical.
- CONGRUENT ANGLES – When two or more angles have the same measure or are identical, they are congruent and also when two angles are congruent they are also equal. The fact holds good for both the ways and for all types of angles, may they be acute, obtuse, right, exterior or interior angles.
What is the symbol of congruency?
You are already aware of the symbol of congruency, which is ≅. If angle A is the same measure as angle B then they are said to be congruent or identical and are symbolically represented as ∠A = ∠B or ∠A ≅ ∠B.
Defining rules of congruency
Congruent angles concept or instead congruency is holding its base on two basic rules.
1. First and mandatory rule is that two angles should have the same angular measurements in order to be congruent.
2. The second rule holds that the size, length or direction of the arms do not matter.
Possible constructions of congruent angles
The congruent angles can be made using a protractor easily. The same can even be constructed with the help of a compass and a ruler. The basic fact and skills to copy the exact degrees of angle.
One of the easiest ways to make congruent angles is to make two parallel lines intersected by a transversal. Then on the basis of the concept of corresponding angles, vertical angles,
alternate angles etc. one can easily name the pairs of congruent angles. Between a set of parallel lines with the same transversal bisecting both the set of congruent angles are:
- Exterior angles
- Interior angles
- Corresponding angles
- Alternate angles
- Vertically opposite angles
This also goes the other way round as using congruent angle theorems the congruent angles can be identified and if the angles are congruent the congruency theorem applies.
What is meant by the congruent supplement theorem?
Do the congruent angles add up to be the sum equal to 180 degrees?
It is a well-known fact that supplementary angles have a sum equal to 180 degrees. The congruent supplement theorem states ‘ angles is a supplement of the other angle if their sum is 180 degrees’. If the two angles are formed on the same straight line with a common arm between them then the sum of those angles forms a linear pair or a 180-degree angle.
A special case: When any line segment is bisected perpendicularly then the angles formed on either side of the bisector are congruent to each other and the measurement of each is equal to a right angle, i.e., 90 degrees and on adding both we get the sum equal to the linear pair of angles,i.e., 180 degrees.
What is the congruent complements theorem?
The angles with a measure of their sum equal to 90 degrees are said to be complementary. the respective theorem states ‘ when two angles are equal and congruent and their sum is equal to a right angle or 90 degrees the congruent complementary theorem applies’.
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Concluding, it is clear that there are various basics theorems and concepts based on congruency.