Congruent Figure
Congruent figures are geometric shapes that have exactly the same shape and the same size. When placed one over the other, they superimpose perfectly, meaning all their corresponding parts are equal.
Key Concepts
Two polygons are congruent if their corresponding sides are equal in length and their corresponding interior angles are equal in measure.
In geometry, the concept of congruence is denoted by an equals sign with a tilde above it.
While all congruent figures are inherently similar figures because they share the same shape, not all similar figures are congruent because they may differ in size.
Common Misconceptions
Myth: Assuming that if two geometric figures have the same area or perimeter, they must be congruent.
Fact: Figures can have the same area but different shapes. For example, a rectangle measuring 4 by 9 units and a square measuring 6 by 6 units both have an area of 36 square units, but they are not congruent.
Real World Applications
Pages of the same printed NCERT textbook are congruent figures because they share the exact same length, width, and rectangular shape.
Coins of the same denomination minted in the same year are congruent, as they have the identical radius and thickness.
Frequently Asked Questions
What is the difference between congruent and similar figures?
Congruent figures have exactly the same shape and size, meaning their corresponding sides and angles are equal. Similar figures have the same shape but can have different sizes, meaning their corresponding sides are proportional.
What are the criteria for congruence of triangles?
The standard criteria to prove two triangles are congruent are Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Right angle-Hypotenuse-Side (RHS).