Congruent Triangles

Congruent triangles are those two triangles which are said to be congruent if and only if one of them can be made to superpose on the other so as to cover it exactly.

Let ∆ABC and ∆DEF be two congruent triangles, then we can superpose ∆ABC on ∆DEF so as to cover it exactly. The vertices of ∆ABC fall on the vertices of ∆DEF in the following order A ↔ D, B ↔ E, C ↔ F.

Thus, the order in which vertices match automatically determines the correspondence between the sides and angles of the triangle. Corresponding parts are also called matching parts of triangles.

So, we have six equalities

Corresponding sides are congruent:   AB = DE          BC = EF          CA = FD         

Corresponding angles are congruent: ∠A = ∠D          ∠B = ∠E          ∠C = ∠F          

In the congruent triangles we will observe six correspondences between their verities. The symbol used to denote correspondence is ‘↔’

A ↔ D             B ↔ E              C ↔ F              written as ABC ↔ DEF

A ↔ E             B ↔ F              C ↔ D              written as ABC ↔ EFD

A ↔ F             B ↔ D              C ↔ E              written as ABC ↔ FDE

A ↔ D             B ↔ F              C ↔ E              written as ABC ↔ DFE

A ↔ E             B ↔ D              C ↔ F              written as ABC ↔ EDF

A ↔ F             B ↔ E              C ↔ D              written as ABC ↔ FED

Therefore, ∆ABC ≅ ∆DEF

Note:

The order of letters in the name of two triangles will indicated the correspondence between the vertices of two triangles. Thus, two triangles are congruent only if there exist a correspondence between their vertices such that the correspondence sides and correspondence angles of two triangles are equal.

Congruent Shapes

Congruent Line-segments

Congruent Angles

Congruent Triangles

Conditions for the Congruence of Triangles

Side Side Side Congruence

Side Angle Side Congruence

Angle Side Angle Congruence

Angle Angle Side Congruence

Right Angle Hypotenuse Side congruence

Pythagorean Theorem

Proof of Pythagorean Theorem

Converse of Pythagorean Theorem

7th Grade Math Problems

8th Grade Math Practice

From Congruent Triangles to HOME PAGE

Recent Articles

• 

1. What is Area in Maths? | Units to find Area | Conversion Table of Area

   Jul 17, 25 01:06 AM

   
   The amount of surface that a plane figure covers is called its area. It’s unit is square centimeters or square meters etc. A rectangle, a square, a triangle and a circle are all examples of closed pla…

   Read More

2. Worksheet on Perimeter | Perimeter of Squares and Rectangle | Answers

   Jul 17, 25 12:40 AM

   
   Practice the questions given in the worksheet on perimeter. The questions are based on finding the perimeter of the triangle, perimeter of the square, perimeter of rectangle and word problems. I. Find…

   Read More

3. Formation of Square and Rectangle | Construction of Square & Rectangle

   Jul 16, 25 11:46 PM

   
   In formation of square and rectangle we will learn how to construct square and rectangle. Construction of a Square: We follow the method given below. Step I: We draw a line segment AB of the required…

   Read More

4. Perimeter of a Figure | Perimeter of a Simple Closed Figure | Examples

   Jul 16, 25 02:33 AM

   
   Perimeter of a figure is explained here. Perimeter is the total length of the boundary of a closed figure. The perimeter of a simple closed figure is the sum of the measures of line-segments which hav…

   Read More

5. Formation of Numbers | Smallest and Greatest Number| Number Formation

   Jul 15, 25 11:46 AM

   In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

   Read More

Word problems on Pythagorean Theorem