Congruence means compatibility. But what does congruence mean in mathematics?In mathematics, we can say that two figures are congruent if they have the same size and shape, even though their orientation or position is different. The coincident parts of the congruent figures are called homologous parts.
In a nutshell, congruent angles are the angles that have equal measure. So, every angle that is equal in measurement will be named congruent angles. They are seen everywhere, for example, in an isosceles triangle, equilateral triangle, or when a transversal intersects two parallel lines.
How to know if two numbers are congruent?
Angles having same measurement are called congruent angle.
If two angles are congruent, it is denoted by the symbol"≅". So, if you want to represent
Let us look at more examples of congruent angles below:
In the above image, both the angles measure 60 degrees. Therefore, they can entirely overall each other. Thus, according to the definition of congruent angles, we can say that both the given angles are congruent
According to the vertical angle theorem, vertical angles are always congruent. Here is proof for you to check through the vertical angle theorem.
Statement: Vertical angles are congruent.
Proof: The proof is based on straight angles. We already know that tips on a straight line add up to 180 degrees.
So, in the above diagram:
Conclusion: Vertically opposite angles are always congruent angles. Hence proven.
The alternate interior angles theorem states that when a transversal cuts 2 parallel lines, the resultant angles are congruent.
In the following figure, if k||l, then <2 ≅ <8 and <3 ≅ <5.
And now we will prove that <2 ≅ <8.
Proof:
By the corresponding angles postulate, <1 ≅ <5 since k||l
Therefore, m<1=m<5 by the definition of congruent angles.
Now, m<1+m<2=180 degrees since <1 and <2 form a linear pair, they are supplementary.
Also, <5 and <8 are supplementary, therefore, m<5+m<8=180 degrees.
We were substituting m<1 for m<5, we get m<1+m<8=180 degrees.
On subtracting m<1 from both sides, we have m<8=180 degrees – m<1= m<2
Therefore, <2≅<8
This way, you can prove that <3≅<5 using the same process.
Supplementary angles are those whose sum is 180 degrees. Thus, the theorem states that angles supplementing the same angle are congruent angles.
We can prove this theorem by using the linear pair property of angles as:
Follow these steps to construct a congruent angle:
Now, let us see how to construct congruent angles:
Here are the tips to understand whether angles are congruent:
If two lines are perpendicular, they form congruent adjacent angles.
Question 1:
Angles 1 and 2 are corresponding. For example, if the measure of angle 2 is 67 degrees, what is the measure of Angle 1?
Answer: When a transversal cuts two parallel lines, the angles on the same side of the transversal and in matching corners will be congruent. Angles 1 and 2 are congruent, so both have an angle measure of 67 degrees.
Question 2:
Line R is a transversal that crosses through the two parallel lines s and t. List all of the angles that are congruent to angle 6.
Question 3:
If the following irregular quadrilaterals are congruent, angle C must be congruent to what other angle?
Corresponding angles are congruent for congruent polygons.
In conclusion,
So, now you clearly understand what a congruent angle is, its theorems, the tips to understand when an angle is called a congruent angle, and their example. Congruent angles are frequently used in construction, art, architecture, and design. So, have an in-depth understanding of congruent angles and have a shining career in architecture.
Ans. Congruent angles are those angles having equal angles.
Ans.Two angles can be called congruent angles when two pairs of corresponding sides and corresponding angles between them are equal.
Ans.If two parallel lines are cut by a transversal, the alternate interior angles are congruent.
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