3. Congruent Triangles in Real Life

Triangles are used everywhere - in buildings, bridges, art and design. In many of these places, we can see congruent triangles (triangles with the same shape and size). Let's look at a few examples.

 

 

 

 

The glass pyramid of the Louvre Museum is made up of several triangular glass panels.

 

The triangular panels are arranged systematically to form the pyramid.

 

• Many triangular panels on the pyramid have the same shape and the same size.
• Some triangles are positioned differently because of the pyramid's structure, but their orientation does not affect congruence.
• If two triangular panels have corresponding sides and angles equal, they are congruent.

 

 

 

Congruent triangular panels create a strong, symmetrical, and attractive pyramid structure.

 

 

 

 

The Egyptian pyramid has triangular faces that meet at the top vertex.

 

The visible side faces have a triangular shape.

 

• A regular square-based pyramid has four triangular side faces. 
• In an ideal regular pyramid, these four triangular faces are congruent because they have the same dimensions.
• Each triangular face has the same slant height and corresponding base side length.
• The triangles may face different directions, but rotation does not change their size or shape.

 

 

The dome is covered with a network of straight rods that form many small triangles.

 

• The rods divide the curved surface into numerous triangular sections. 
• Several of these triangular sections may have the same side lengths and the same shape.
• Such triangles are congruent even though they are located in different parts of the dome.
• Triangular frameworks are useful in construction because triangles provide stability and help distribute forces.

 

 

 

 

 

The rangoli contains several coloured triangular regions arranged around a central point. Some triangles are repeated in different positions and orientations.

 

• Several blue and pink triangular regions appear to have the same size and shape. 
• Some triangles are rotated or reflected versions of others.
• Rotation and reflection do not change the size or shape of a triangle.
• Therefore, triangles that match exactly after being moved, rotated, or flipped are congruent.

 

 

 

Congruent triangles make rangoli designs symmetrical, balanced, and visually attractive.

 

 

 

 

The bridge has a framework made of straight steel members. These members form many triangular shapes in the supporting trusses.

 

• The bridge contains repeated triangular sections in its framework. 
• Several triangles in corresponding parts of the truss may have the same dimensions.
• These triangles can be congruent when their corresponding sides and angles are equal.
• Triangular frameworks are widely used in bridges because triangles maintain their shape and provide structural stability.

 

 

 

Repeated triangular frameworks in bridges help provide strength, stability, and an organised design.