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Rectangular Pyramids

Is the sum of the squares of two opposite sloping edges of a rectangular based pyramid equal to the sum of the squares of the other two sloping edges?

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Rhombus in Rectangle

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.

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Similarly So

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

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Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Created with GeoGebra
Triangle ABC is any right angled triangle and X is a moveable point on the hypotenuse AC. The points P and Q are the feet of the perpendiculars from X to the sides of the triangle.

Find the position of X which makes the length of PQ a minimum.
NOTES AND BACKGROUND

This dynamic image is drawn using Geogebra, free software and very easy to use. You can download your own copy of Geogebra from http://www.geogebra.org/cms/ together with a good help manual and Quickstart for beginners.


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. More information on many of our other activities can be found here.
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