In Mathematics, the word congruent is used to show identical figures. It means two or more figures will be congruent if they have exactly the same shape and size. To be congruent, the shapes shouldn’t have a difference of millimeters in size and shape.
If two figures are congruent, they can be flipped over each other without finding a single difference. Simply, these figures can be placed precisely over each other to have a single preview from a distance.
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Real-life examples of Congruent
In real life, we can understand this term and its definition easily. Let us show you some examples from real life.
- Two pieces of bread.
- Two cubes of the same size.
- Two or more chairs from a single set
Representation of Congruence
To show congruence between two or more figures, a specific symbol is used. The symbol is made by combining two common symbols that we call a tilde and an equal. Here is the final symbol that shows two or more figures are congruent “≅”.
This symbol is inserted between the names of the figures. For example, two shapes named “A” and “B” are represented as A ≅ B.
Are congruent and similar shapes the same?
When it comes to plain English, the common term “similar” is used to recall the same images. Many people think that similar figures are also called congruent figures. It is not right because congruent means identical while similar means to have matched sections.
So, it is wrong to say that similar images are also congruent because such images don’t fulfill the requirements of being congruent.
Terms related to congruence in Geometry
On the basis of being congruent, multiple terms are defined in Geometry. Let us explain a few important figures for understanding.
Read about Altitude in Geometry here.
- Congruent Lines
If we draw two lines on the same base with the same length and angles, these are called congruent lines. For example, two perpendicular lines are drawn on a single base with the same length.
Read about Perpendicular Lines here.
- Congruent Circles
Two circles are said to be congruent if they have a radius of the same length. For example, if the radius of two circles is 5 cm, it means both circles are congruent to each other.
Read about Circle here.
- Congruent Triangles
Triangle is one of the most used figures in Geometry. Two or more triangles can also be congruent if the length of all three sides as well as the measures of all three angles are the same in both triangles.
Read about Acute Triangle here.
What is the condition of being congruent?
The only condition for being congruent is being identical. It means that the figures should be equal in size and shape.
Can congruent shapes have different dimensions?
No, the shapes with different dimensions can’t be congruent.
Are all congruent figures similar figures?
Yes, all congruent figures are called similar figures but not all similar figures can be termed congruent figures.
How to prove that triangles are congruent?
To prove that triangles are congruent, you need to measure the angles and lengths of the sides. If all three sides and angles are equal in both triangles, it shows that the triangles are equal to each other.
Is there another name for the congruent term in Mathematics?
Yes, congruent shapes are also termed “Identical shapes” in Mathematics and Physics.