ABCDE is a regular pentagon of side length one unit. BC produced
meets ED produced at F. Show that triangle CDF is congruent to
triangle EDB. Find the length of BE.
Three triangles ABC, CBD and ABD (where D is a point on AC) are all
isosceles. Find all the angles. Prove that the ratio of AB to BC is
equal to the golden ratio.
The diagram shows a regular pentagon with sides of unit length.
Find all the angles in the diagram. Prove that the quadrilateral
shown in red is a rhombus.
Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.
Measure the two angles. What do you notice?
Triangle ABC has a right angle at C. ACRS and CBPQ are squares. ST
and PU are perpendicular to AB produced. Show that ST + PU = AB
The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?
This LOGO Challenge emphasises the idea of breaking down a problem
into smaller manageable parts. Working on squares and angles.
Make five different quadrilaterals on a nine-point pegboard,
without using the centre peg. Work out the angles in each
quadrilateral you make. Now, what other relationships you can see?
An equilateral triangle rotates around regular polygons and
produces an outline like a flower. What are the perimeters of the
Points D, E and F are on the the sides of triangle ABC.
Circumcircles are drawn to the triangles ADE, BEF and CFD
respectively. What do you notice about these three circumcircles?
Creating designs with squares - using the REPEAT command in LOGO.
This requires some careful thought on angles
Can you work out where the blue-and-red brick roads end?
Prove that the internal angle bisectors of a triangle will never be
perpendicular to each other.
Interior angles can help us to work out which polygons will
tessellate. Can we use similar ideas to predict which polygons
combine to create semi-regular solids?
This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.
The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .
More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.
Turn through bigger angles and draw stars with Logo.