Practical Geometry

# Practical Geometry

Practical Geometry involves the construction of various shapes and sizes, making it a fundamental branch of geometry. It introduces us to a range of two-dimensional and three-dimensional shapes. In practical geometry, we acquire the skills to accurately draw these shapes while maintaining their proper dimensions.

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## Practical Geometry – Construction of Parallel Lines

Two lines are considered parallel if they never intersect or meet at a single point. Parallel lines extend infinitely in both directions and can be represented by the symbol ‘||’. Real-life examples of parallel lines include railway tracks and the edges of a ruler.

In practical geometry, the only tools needed to draw a line parallel to another line are a ruler and compass. To learn the step-by-step process of drawing parallel lines, you can click here.

## Practical Geometry – Construction of Triangle

A triangle is a closed geometric shape characterized by three sides and three angles. The key properties that define triangles include:

• The sum of all three interior angles in a triangle is always equal to 180 degrees.
• An exterior angle of a triangle is equal to the sum of the two interior opposite angles.
• The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
• In a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides, known as the adjacent side and the perpendicular side.

To construct a triangle, specific conditions must be satisfied based on the above properties, including:

1. Knowing the lengths of all three sides of the triangle.
2. Having knowledge of two sides and the included angle between them.
3. Being aware of two angles and the included side between them.

For a right triangle, the essential information required for construction includes knowing the lengths of the hypotenuse and one of the legs.

## Practical Geometry – Constructing triangle (SSS Criterion)

Constructing a triangle is a process when we know the lengths of all three sides. Here are the steps to create a triangle:

1. Select one of the sides as the base of the triangle, which means you already know the two endpoints of the base.
2. Using a ruler and compass, measure the length of another side of the triangle and mark a point above the base.
3. Once you’ve marked the appropriate distance, draw an arc above the base using the compass.
4. Next, measure the length of the third side of the triangle using the ruler and compass, and make a mark on the arc.
5. The point where the arc intersects with the mark for the third side is your third vertex, completing the construction of the triangle

## Practical Geometry – Constructing triangle (SAS Criterion)

In the Side-Angle-Side (SAS) condition, we can construct a triangle when we know two sides of the triangle and the angle between them.

1. Begin by selecting one of the given sides as the base of the triangle. This immediately provides us with two known vertices of the triangle.
2. Using one of these vertices as the center, with the help of ruler and protractor to accurately measure the specified angle. Mark this point on the paper as it will be one of the triangle’s vertices.
3. Now, still using the same vertex as the center, use a compass to measure the length of the other given side of the triangle. Then, draw an arc from the marked vertex to obtain the location of the third vertex.
4. Finally, join the three vertices to complete the construction of the triangle.

### Practical Geometry – Constructing Triangle (ASA Criterion)

The ASA criterion for triangles is similar to the SAS criterion. In ASA, we are provided with two angles of the triangle and the side located between these angles. Using this process, we can proceed to construct the triangle.

• Similar to other triangle constructions, the process begins with drawing the base of the triangle based on the given side.
• Next, using a protractor, place it at both ends of the baseline (the vertices of the triangle) and measure the two provided angles.
• By connecting the points to their respective vertices and extending these lines, we can identify the intersection point of the two lines.
• This point serves as the third vertex of the triangle. As a result, we have successfully constructed a triangle.

### Practical Geometry – Constructing Triangle (RHS Criterion)

As we know a right triangle is a type of triangle in which one of its angles measures precisely 90 degrees. According to the RHS criterion, it is possible to create a right triangle when we have information about both the length of its hypotenuse side and the length of either of its leg-sides (either the perpendicular side or the adjacent side).

## FAQs on Practical Geometry

### What is the concept of practical geometry?

Practical geometry is a branch of geometry that focuses on applying geometric principles to solve real-world problems and construct various shapes and figures using tools like a compass, ruler, and protractor.

### What are the practical uses of geometry?

Geometry has many practical applications, including architecture, engineering, design, cartography (map-making), navigation, computer graphics, and even in everyday tasks like measuring, cutting, and building.

### What do I learn in the chapter practical geometry?

In a chapter on practical geometry, you typically learn how to use geometric concepts and tools to construct and solve problems involving lines, angles, triangles, circles, and other geometric shapes.

### What is practical geometry?

Practical geometry is the application of geometric principles to solve real-world problems, design objects, and construct various geometric shapes accurately.

### Who is the father of practical geometry?

Euclid, a Greek mathematician from around 300 BCE, is often regarded as the father of practical geometry because his work Elements laid the foundation for geometry as we know it today, including its practical applications.

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