A triangle is a closed figure that has three sides, three vertices and three angles. Two triangles are said to be congruent when their three corresponding angles or sides are equal in measure. We have 5 congruency rules to say that two triangles are congruent. That Triangle Congruence conditions and examples are listed here.

## Congruence in Triangles

Congruence is the term used to define an object and its mirror image. Two objects are called congruent if their shapes and dimensions are the same. In geometry and measurement, line segments having the same length and angles with the same measure are congruent.

The following are the conditions that are useful to say two triangles are congruent. The geometrical shapes are repositioned or flipped or rotated to coincide with other shapes. Corresponding Parts of Congruent triangles is a technique that says the different rules of congruency along the lines.

• SSS (Side Side Side)
• SAS (Side Angle Side)
• ASA (Angle Side Angle)
• AAS (Angle Angle Side)
• RHS (Right angle Hypotenuse Side)

### Congruency of Triangles by Same Side, Same Angle

If two triangles are congruent when they have exactly the same three sides and same three angles. There is no need to equal sides and angles in the same position, but it can be turned or flipped.

Same Sides

When the sides of two triangles are the same, then those are congruent.

In the above figure, triangle 1 is congruent to triangle 2. Because their sides have exactly the same side length.
But triangle 1 or triangle 2 is not congruent to triangle 3 as they have different side lengths.

Same Angles

In the above figure, the first triangle is congruent to the second triangle as they have the same angles.
But the second triangle is not congruent to the third triangle as they do not have exactly the same angles.

### Example Questions on Triangle Congruence

Example 1:
Decide whether the following triangles are congruent or not and give the reason.

Given two triangles are △ABC, △ACD
In both triangles AD ≅ BC, AC ≅ AC and AB ≇ CD
So, △ABC ≇ △ACD

Example 2:
Decide whether the following triangles are congruent or not and give the reason.

Given two triangles are △ABC, △DEF
In both triangles ∠A ≅ ∠E, ∠C ≅ ∠F and ∠B ≅ ∠D
So, △ABC ≅ △DEF

### FAQ’s on Congruency of Triangles

1. What is congruence of a triangle?

Two triangles are congruent menats they have corresponding sides of equal length and their corresponding anglres are equal in measure.

2. What are 5 congruence criteria for triangles?

Two triangles are said to be congruent if they satisfy these 5 conditions. They are side-side-side (SSS), side-angle-side (SAS), angle-angle-side (AAS), angle-side-angle (ASA), and right angle hypotenuse side (RHS).

3. What happens when two traingles are congruent?

When two triangles are congruent then they will have exactly the same three sides and same three angles.

4. What are the 3 properties of congruence?

The three properties of congruence are reflexive property, symmetric property and transitive property.