Fundamentals of Triangle Construction

Yes, they do. Adding any two sides gives a sum greater than the third side ($4$ cm + $5$ cm > $6$ cm, $5$ cm + $6$ cm > $4$ cm and $4$ cm + $6$ cm > $5$ cm).

Possible angle measurements could be 50°, 60° and 70°, as long as their total equals 180°.

To construct this triangle, you would need a ruler to measure and draw the sides accurately, and a protractor to measure and draw the angles, ensuring they add up to 180 degrees. You could also use a compass to help you construct this triangle but it isn’t necessary if you have a ruler and a protractor.

A triangle cannot be formed because the sum of two sides ($2$ cm + $2$ cm) is not greater than the length of the third side ($5$ cm), violating the triangle inequality rule.

If you tried drawing this triangle, the sides wouldn't meet to form a closed shape, resulting in an open figure rather than a triangle.

If you tried to make a model of a triangle with these lengths, you would find that the two shorter sides (each $2$ cm) are not long enough to connect when trying to reach around the longer side ($5$ cm). This means you wouldn't be able to form a closed triangular shape.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

This condition ensures that the sides can meet to form a closed shape. If the sum of two sides is equal to or less than the third side, the sides cannot form a triangle.

No, in Euclidean geometry, the sum of the interior angles of a triangle is always exactly 180 degrees.

If the sum of the angles is not 180 degrees, then the figure cannot be a triangle. The angles must precisely total 180 degrees for it to be a valid triangle.

The angles of a triangle can be measured using a protractor, a tool used in geometry to measure angles.

Triangles can be classified by their sides (scalene, isosceles, equilateral) and by their angles (acute, obtuse, right angled).

No, a triangle cannot have all obtuse angles. It can have at most one obtuse angle.

No, not with any three line segments. The lengths must satisfy the condition that the sum of any two sides is greater than the third side.

Understanding how to construct triangles is fundamental in geometry as it forms the basis for understanding more complex shapes and theorems.

Yes, triangle construction principles are widely used in real-life situations. For example, engineers and architects use these principles when designing bridges, roofs and other structures to ensure stability and balance. In art and design, understanding triangles helps in creating visually appealing and structurally sound compositions. Even in everyday problem-solving, such as determining the shortest path between points, triangle principles can be applied.