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.
By definition, two figures, object or shape are said to be congruent if they have same shape or size as the mirror image of the other. The congruent shape superimpose each other. This simply means that they can be placed completely over each other.
For example, two squares with side 5 cm each are congruent to each other, as they can completely overlap each other. Below is the illustration for the same:
Geometric Concepts Related to Congruency
To understand relationship between shapes and make deductions about their properties,we need to identify congruency in any geometrical shape. Following are some geometrical concepts related to congruency:
- Line Segment: Two lines are congruent and they will have same properties if their length is same.
- Angles: Two angles will be congruent, if they have same measure.
- Circle: Two circles are congruent if they have same diameter.
Overall, in order to find congruency in any geometrical shape, we need to identify them using different parameters, For example in case of polygons, we first match the vertices and then move towards sides and angles to find similarity. Let us discuss more on identifying congruent figures in detail.
Identifying Congruent Figures
Congruent figures do have some differences, but in terms of properties they tend to have same measures which help us in analyzing two shapes accurately. To identify congruent figures in any polygon, we can follow the following steps
Step 1: Check the type of 2-dimensional shape(triangle, hexagon, etc) by counting the number of vertices.
Step 2: Check the length of all sides of the figure.
Step 3: Check the measure of all angles of the figure.
If all the measures of the given figures are same, then the given figures are congruent to each other.
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
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