Congruent
In geometry, congruent refers to identical in shape and size. Congruent figures or objects have the same shape and size, or in other words, if one object has the same shape and size as the mirror image of the other then they are congruent. There are many theorems associated with congruency and equality. Two line segments are congruent if and only if they have equal measures. Two angles are said to be congruent if and only if they have equal measures. Two triangles are congruent if and only if their corresponding parts are equal.
1.  Congruent Definition in Geometry 
2.  What is Congruence? 
3.  Properties of Congruence 
4.  Solved Examples on Congruent 
5.  Practice Questions on Congruent 
6.  FAQs on Congruent 
Congruent Definition in Geometry
The word "congruent" means exactly equal in every aspect of a figure in terms of shape and size. Even if we turn or flip the shapes or rotate the shapes, they remain congruent. Suppose we draw two circles of the same radius on a piece of paper and cut them out and match them up completely we will notice that they are of the same shape and size or we can say they are congruent. The symbol "≅" means one thing is congruent to another. If the angles of one shape are equal to another then angles are also congruent in nature. Similarly, if the sides of one shape are equal in length corresponding to another shape then the sides are also congruent in nature.
What is Congruence?
The word congruence is used to describe the relation of two figures that are congruent. Congruent figures have the same shape and size (informally) whereas congruence satisfies many of the properties of equality. If we consider the same example of a circle having equal radii then the two circles are congruent. If two geometrical figures are congruent, they can be exactly superimposed upon each other. Look at the image given below, the figures are congruent in nature.
If circle A is congruent to circle B, we will write this fact as follows: A ≅ B.
Properties of Congruence?
Following are the properties of congruence: Reflexive property, Symmetric property, and Transitive property.
 In congruence, reflexive property means a line segment or angle or shape is congruent to itself. For example, ∠P≅∠P for any angle P
 In congruence, the symmetric property says that if one figure is congruent to another, then the second one is also congruent to the first. For any two angles P and Q, ∠P ≅∠Q, then ∠Q ≅∠P.
 Transitive property of congruence states that if two lines or angles or shapes are congruent to the third, then the first two lines or angles or shapes are congruent. If A ≅ B and B ≅ C, then A ≅ C.
Congruence of Triangles
Two triangles are said to be congruent if their sides have equal lengths and angles are equal in measures and they can be superimposed on each other.
In the above figure, Δ ABC and Δ PQR are congruent triangles. This means that the corresponding angles and corresponding sides in both the triangles are equal.
Vertices: A and P, B and Q, and C and R are the same.
Sides: AB = PQ, BC = QR and AC= PR;
Angles: ∠A = ∠P, ∠B = ∠Q, and ∠C = ∠R.
Δ ABC ≅ Δ PQR
Note: The following are the ways to find if two triangles are congruent.
 SSS (side, side, side)
 SAS (side, angle, side)
 ASA (angle, side, angle)
 AAS (angle, angle, side)
 RHS (Right angleHypotenuseSide)
Congruent Shapes
When one shape is placed over the other and if they superimpose one over the other, they are said to be congruent. They match exactly even if they are rotated or flipped. The square is the only shape that has all congruent sides and all angles are congruent because square property says all the sides of the square are equal and angles are also equal.
Important Notes
 Two figures are congruent if they have the same shape and size.
 Two angles are congruent if their measures are exactly the same.
Related Articles on Congruent
Check out these interesting articles to know more about congruent.
Solved Examples on Congruent

Example1: The two quadrilaterals are congruent.
Which angle in quadrilateral PQRS corresponds to ∠QRS in quadrilateral ABCD?
Solution:
Let us identify the corresponding parts in both quadrilaterals.
∠QRS is marked with four arcs.
∠WXY is also marked with four arcs.This shows that ∠QRS coincides with ∠WXY. So ∠WXY corresponds to ∠QRS.

Example2: In the given figure which side in quadrilateral PQRS corresponds to YZ in quadrilateral WXYZ?
Solution:
Let us identify the corresponding parts in both quadrilaterals.
YZ is adjacent to the angles marked with one arc and two arcs.
PQ is also adjacent to the angles marked with one arc and two arcs.This shows that PQ coincides with YZ, So PQ corresponds to YZ.

Example3: Emma is doing craftwork. She has four squares with given sides, Square A = 5inches, Square B = 7inches, Square C = 5inches, Square D = 8 inches
She wants two squares that can be placed exactly one over the other. Can you help her choose?Solution: Squares with the same sides will superimpose on each other. So, Emma should find two squares whose side lengths are exactly the same. Such shapes are congruent. In the given list we can see that Square A and Square C are of the same size that is 5 inches. She can take Square A and C as they can be placed exactly one over the other.
FAQs on Congruent
How do you Prove a Shape is Congruent?
Two shapes are congruent if they are exact copies of each other and cover each other exactly when they are superimposed.
How Do You Know if a Triangle is Congruent?
Two triangles are said to be congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.
What Shape Has All Congruent Sides?
The square has all congruent sides and all angles are congruent because according to square property all the sides of the square are equal and angles are also equal.
What are the 5 ways to Prove Congruence in Triangles?
The belowmentioned list shows the ways to prove the two triangles congruent.
 SSS (side, side, side)
 SAS (side, angle, side)
 ASA (angle, side, angle)
 AAS (angle, angle, side)
 RHS (Right angleHypotenuseSide)
Are Vertical Angles Always Congruent?
When two lines intersect vertical angles are formed. The angles opposite to each other are equal. Vertical angles are always congruent because according to the vertical angles theorem, they are equal in measure therefore they are congruent too.
What is Another Word for Congruent?
Congruent refers to identical in shape and size. Congruent shapes are also called coinciding shapes.
What Makes the Angles Congruent?
Angles are said to be congruent if their measures are exactly the same in degrees or radians. If ∠P = ∠Q, then both the angles are said to be congruent angles.