Nalanda College, Colombo 10 Grade 11 Maths Worksheet: 11 Midpoint Theorem

Perimeter of the triangle formed by joining three midpoints

Answer: 12 cm

💡 What it's asking: Joining the three midpoints makes a smaller triangle. By the midpoint theorem, each of its sides is exactly half of one side of the big triangle.

1. 1The midpoint theorem: a line joining two midpoints is parallel to the third side and half its length.
2. 2So the small triangle's sides are half of XYZ's sides: 5 cm, 4 cm and 3 cm.
3. 3Perimeter = 5 + 4 + 3 = 12 cm.

✅ Every side is halved, so the perimeter should be half of XYZ's perimeter; 12 is half of 24.

Midpoint segment length after finding the third side from perimeter

Answer: 12 cm

💡 What it's asking: XY joins the midpoints of AC and BC, so it is half of AB. But AB isn't given, so find it from the perimeter first.

1. 1Perimeter 58 = AB + 18 + 16, so AB = 58 − 18 − 16 = 24 cm.
2. 2X and Y are midpoints of AC and BC, so XY is parallel to AB and half of it.
3. 3XY = 24 ÷ 2 = 12 cm.

✅ XY should be shorter than AB and parallel to it in the figure; 12 is half of 24.