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.

Congruent Triangles

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




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



Share this page: What’s this?

Recent Articles

  1. Months of the Year | List of 12 Months of the Year |Jan, Feb, Mar, Apr

    Apr 20, 24 05:39 PM

    Months of the Year
    There are 12 months in a year. The months are January, February, march, April, May, June, July, August, September, October, November and December. The year begins with the January month. December is t…

    Read More

  2. What are Parallel Lines in Geometry? | Two Parallel Lines | Examples

    Apr 20, 24 05:29 PM

    Examples of Parallel Lines
    In parallel lines when two lines do not intersect each other at any point even if they are extended to infinity. What are parallel lines in geometry? Two lines which do not intersect each other

    Read More

  3. Perpendicular Lines | What are Perpendicular Lines in Geometry?|Symbol

    Apr 19, 24 04:01 PM

    Perpendicular Lines
    In perpendicular lines when two intersecting lines a and b are said to be perpendicular to each other if one of the angles formed by them is a right angle. In other words, Set Square Set Square If two…

    Read More

  4. Fundamental Geometrical Concepts | Point | Line | Properties of Lines

    Apr 19, 24 01:50 PM

    Point P
    The fundamental geometrical concepts depend on three basic concepts — point, line and plane. The terms cannot be precisely defined. However, the meanings of these terms are explained through examples.

    Read More

  5. What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral

    Apr 19, 24 01:22 PM

    Square - Polygon
    What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments.

    Read More

Word problems on Pythagorean Theorem