- Verify the triangle inequality for each set of side lengths: the sum of any two sides must be greater than the third side.
- For problem 1 (7cm, 5cm, 9cm): 7+5>9, 7+9>5, 5+9>7 → valid.
- For problem 2 (2.5cm, 2.5cm, 2.5cm): equilateral, all sums > third side → valid.
- For problem 3 (4cm, 7.5cm, 8cm): 4+7.5>8, 4+8>7.5, 7.5+8>4 → valid.
- For problem 4 (3.8cm, 4.2cm, 6.2cm): 3.8+4.2>6.2, 3.8+6.2>4.2, 4.2+6.2>3.8 → valid.
- For problem 5 (1.7cm, 8.2cm, 7.2cm): 1.7+7.2=8.9>8.2, 1.7+8.2>7.2, 7.2+8.2>1.7 → valid.
- For problem 6 (6.6cm, 6.6cm, 6.6cm): equilateral → valid.
- For problem 7 (9.2cm, 3.5cm, 8.4cm): 3.5+8.4=11.9>9.2, 3.5+9.2>8.4, 8.4+9.2>3.5 → valid.
- For problem 8 (3.7cm, 3.9cm, 5.2cm): 3.7+3.9>5.2, 3.7+5.2>3.9, 3.9+5.2>3.7 → valid.
- All given sets satisfy the triangle inequality, so all triangles can be constructed.
- To construct each triangle: draw one side with a ruler, use a compass to draw arcs from both endpoints with radii equal to the other two sides, and connect the intersection point to the endpoints.
Parent Tip: Review the logic above to help your child master the concept of basic construction math worksheet.
