Comparing Quantities | Class 7 Mathematics Notes

7.2 Constructing a Triangle When its Sides are Given

Constructing a triangle when all three side lengths are given involves a method similar to that used for equilateral triangles but adapted for different lengths. Choose one side as the base (e.g., AB = 4 cm). Using a compass, draw an arc of radius equal to the second side length (e.g., 5 cm) centered at A. Then, draw another arc of radius equal to the third side length (e.g., 6 cm) centered at B. The intersection point of these two arcs is the third vertex C. Joining points A, B, and C completes the triangle. This method ensures that the sides AC and BC have the correct lengths. The process can be repeated for various sets of side lengths to construct different triangles. However, not all sets of lengths can form a triangle; the triangle inequality must be satisfied for a valid triangle to exist.

📊 Diagram: Steps showing base AB = 4 cm, arcs of radius 5 cm from A and 6 cm from B intersecting at C; See figure_9, figure_10, figure_11, figure_12.

🧪 Activity: Construct triangles with given side lengths such as (4,4,6), (3,4,5), (1,5,5), (4,6,8), and (3.5,3.5,3.5).

🔗 Connection: This section leads to exploring the conditions under which triangles exist, introducing the triangle inequality.