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Triangle Midpoints

Age 14 to 16
Challenge Level Yellow starYellow star
Secondary curriculum
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Triangle Midpoints printable sheet
 


Given the three midpoints of the sides of a triangle, can you find a way to construct the original triangle?

For example:


Choose any three points.
Can you construct a triangle such that your three points are the midpoints of its sides?

Is there more than one possible triangle for any given set of midpoints?

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Fitting In

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest equilateral triangle which fits into a circle is LMN and PQR is an equilateral triangle with P and Q on the line LM and R on the circumference of the circle. Show that LM = 3PQ

Look Before You Leap

Can you spot a cunning way to work out the missing length?

Two Ladders

Two ladders are propped up against facing walls. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second wall. At what height do the ladders cross?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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