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. Worksheet on Average | Word Problem on Average | Questions on Average

   May 19, 25 02:53 PM

   
   In worksheet on average we will solve different types of questions on the concept of average, calculating the average of the given quantities and application of average in different problems.

   Read More

2. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

   May 18, 25 04:33 PM

   
   In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

   Read More

3. How to Find the Average in Math? | What Does Average Mean? |Definition

   May 17, 25 04:04 PM

   
   Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

   Read More

4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

   May 17, 25 03:47 PM

   Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

   Read More

5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

   May 16, 25 11:13 AM

   
   Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

   Read More

Word problems on Pythagorean Theorem