What is Congruency?

Congruency explains the relation between two shapes or geometric figures. It plays an important part in analyzing and understanding the relation between two geometric figures. In Mathematics, if two shapes are mirror images of each other, they are said to be congruent shapes.

Congruency means identical shape and size, be it a line segment, any geometrical shape, or an angle. In other words, if two shapes have corresponding sides and angles equal they are known as congruent shapes. The two shapes can be superimposed on each other, side to side and corresponding angle to angle.

Congruency Definition

Congruency means exactly equal shape and size. If any shape can overlap each other and appear to be similar, is known as congruent. Mathematically, it is represented by ≅ sign.

Significance of Congruency in Mathematics

Congruency holds vital importance in mathematical field. Following are some applications of congruency:

  • It helps in analyzing shapes and its properties.
  • It is useful in calculating accurate measurements.
  • It is used in various trigonometric solutions.

Congruency

Congruency is a mathematical term that means two or more objects have the same shape and size or if one is the mirror image of the other.

In this article, we will understand the basic geometric concept of congruency, how they are related, their types, some practical applications of congruency, and solve some problems in trigonometry.

Table of Content

  • What is Congruency?
  • Type of Congruency
  • Properties and Characteristics of Congruent Figures
  • Congruent and Similar Figure

Similar Reads

What is Congruency?

Congruency explains the relation between two shapes or geometric figures. It plays an important part in analyzing and understanding the relation between two geometric figures. In Mathematics, if two shapes are mirror images of each other, they are said to be congruent shapes....

Congruency in Geometry

In geometry, congruency is used to identify similar shapes. Even if a shape is rotated or flipped, the congruent shapes remain same....

Type of Congruency

Congruency can be of different types depending upon its geometrical shape. Congruency can be defined in line segments with same length, angles with same measure, triangles where sides and angles are equal, circles with same diameter or radius, etc. Depending upon the identification of Congruency, it is divided into three major types....

Congruency in Triangle

Congruent triangles are triangles that are perfect copies of one another. Two triangles are said to be congruent if and only if they can be overlapped with each other completely. Two triangles are said to be congruent if they have equal corresponding angles or sides....

Properties and Characteristics of Congruent Figures

Two figures which overlap on each other with identical shape and dimension are known as congruent figures. However, Properties and characteristics of congruent figures are different depending upon the figure i.e if the figure is a line segment, an angle, circle or any other polygonal shape....

Practical Applications of Congruency

Congruency can be useful in various aspects of life, it plays major role in architecturul design, engineering and mantaining accuracy in measurements, specially in computer graphics and animation. Practical Applications of Congruency also expand to the field of mathematics, where it is used in solving geometric and trignometry problems....

Congruent and Similar Figure

Congruent Figures and Similar figures are different from each other. Congruent figures refers to the figures that have the equal measure of sides and angles. On the other hand, similar figures may have the same shape, but their size may not be the same....

Solving Problems On Congruency

Example 1: ABCD is a square, where AC is diagonal. Prove that triangle, ABC and CDA are congruent?...

Congruency Frequently Asked Questions

What are Congruent Figures?...

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