Question

Construct the triangle ABC where AB = 6cm, BC = 4cm, AC = 5cm

Answer 1

To construct triangle ABC, draw a 6cm line for AB, use a compass to create 5cm and 4cm arcs from points A and B respectively, and connect the intersection to A and B.

Step-by-step explanation:

To construct a triangle ABC with sides AB = 6cm, BC = 4cm, and AC = 5cm, you can follow these steps:

1. Draw a base line segment AB to the length of 6cm using a ruler.
2. From point A, use a compass to draw an arc with a radius of 5cm, which is the length of AC.
3. Similarly, from point B, draw another arc with a radius of 4cm, which is the length of BC.
4. The intersection point of the two arcs will be point C. Connect point C to points A and B to form the triangle ABC.

This process utilizes the properties of triangles and the fact that the sum of the lengths of any two sides must be greater than the length of the third side, which is satisfied in this case (6+5 > 4, 4+5 > 6, and 4+6 > 5).