Resources tagged with: Angle properties of polygons

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Broad Topics > Angles, Polygons, and Geometrical Proof > Angle properties of polygons

Golden Triangle

Age 16 to 18
Challenge Level

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.

Pentakite

Age 14 to 18
Challenge Level

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.

Pent

Age 14 to 18
Challenge Level

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.

Darts and Kites

Age 14 to 16
Challenge Level

Explore the geometry of these dart and kite shapes!

At a Glance

Age 14 to 16
Challenge Level

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it?

A Sameness Surely

Age 14 to 16
Challenge Level

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

Making Sixty

Age 14 to 16
Challenge Level

Why does this fold create an angle of sixty degrees?

Angles in Three Squares

Age 14 to 16
Challenge Level

Drawing the right diagram can help you to prove a result about the angles in a line of squares.

Floored

Age 14 to 16
Challenge Level

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

Semi-regular Tessellations

Age 11 to 16
Challenge Level

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Road Maker 2

Age 16 to 18 Short
Challenge Level

Can you work out where the blue-and-red brick roads end?

Tricircle

Age 14 to 16
Challenge Level

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. . . .

Arclets Explained

Age 11 to 16

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.

No Right Angle Here

Age 14 to 16
Challenge Level

Prove that the internal angle bisectors of a triangle will never be perpendicular to each other.

Pegboard Quads

Age 14 to 16
Challenge Level

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?

Terminology

Age 14 to 16
Challenge Level

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

Cyclic Quadrilaterals

Age 11 to 16
Challenge Level

Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

Triangles and Petals

Age 14 to 16
Challenge Level

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Dodecawhat

Age 14 to 16
Challenge Level

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.

LOGO Challenge 4 - Squares to Procedures

Age 11 to 16
Challenge Level

This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.

Logo Challenge 3 - Star Square

Age 7 to 16
Challenge Level

Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles

First Forward Into Logo 9: Stars

Age 11 to 18
Challenge Level

Turn through bigger angles and draw stars with Logo.

First Forward Into Logo 7: Angles of Polygons

Age 11 to 18
Challenge Level

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.