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Interval joining the midpoints of two sides of a triangle

Investigate the relationship between an interval joining the midpoints of two sides of a triangle and the third side. Click and drag any of the blue points to change the size and orientation of the triangle ABC.

1. Click the check-box for the interval joining the midpoints of AB and BC. What does the relationship between <BDE and <BAC tell you about the sides DE and AC? Does the ratio of the length of DE to AC change for differing positions of A, B and C?
2. Examine the results for the intervals joining the midpoints of the other two sides. What is the relationship between an interval joining the midpoints of two sides of a triangle and the third side?

© State of New South Wales, Department of Education, 2018