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triangle

Primary Information
Secondary Information

Definition

A triangle is a polygon with three sides and three angles. The sides of a triangle must be straight lines, and the angles must add up to 180 degrees.

Triangles are one of the most basic shapes in geometry. They are used in a variety of applications, including engineering, architecture, and construction.

Triangles can be classified by their side lengths and by their angle measures. Side lengths can be equal or unequal, and angle measures can be acute, obtuse, or right.

Some of the properties of triangles include:

  • The sum of the angles in a triangle is always 180 degrees.
  • The longest side of a triangle is opposite the largest angle.
  • The height of a triangle is the perpendicular distance from a vertex to the opposite side.
  • The area of a triangle is equal to (1/2) × base × height.

How can the word be used?

The triangle has three angles.

triangle

Different forms of the word

Noun:

a closed figure with three straight sides and three angles.

Adjective:

having three sides or angles.

Etymology

The word "triangle" comes from the Greek word "triagōnon", which means "three-angled".

The first recorded use of the word "triangle" in English was in the 14th century.

The word "triangle" is a Greek word, and it is related to the Latin word "triangulum".

Question

Look around the room. What objects contain triangles?

AQA Science Exam Question and Answer

Question:

Explain the concept of a triangle and its significance in geometry. Describe the characteristics of different types of triangles based on their angles and sides. Provide an example of a real-world application where the properties of triangles are utilised.

Answer:

In geometry, a triangle is a polygon with three sides and three angles. Triangles are fundamental shapes in mathematics and have a wide range of applications in various fields.

Triangles are classified based on their angles and sides. According to angles, triangles can be categorized as acute (all angles less than 90 degrees), obtuse (one angle greater than 90 degrees), or right (one angle equal to 90 degrees). Based on sides, triangles can be equilateral (all sides and angles are equal), isosceles (at least two sides and angles are equal), or scalene (all sides and angles are different).

Triangles play a significant role in architecture and engineering. One practical application is in the construction of trusses, which are used to support roofs, bridges, and other structures. Trusses often consist of interconnected triangles that distribute and manage forces efficiently. This design helps to ensure stability and strength, allowing structures to withstand various loads and conditions.

For example, in the construction of a bridge, triangular truss elements are strategically placed to distribute the weight of the bridge and its traffic. The inherent stability and strength of triangles make them an ideal choice for such applications.