Resources tagged with: Angle properties of polygons

Filter by: Content type:
Age range:
Challenge level:

There are 31 results

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

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

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?

Making Sixty

Age 14 to 16 Challenge Level:

Why does this fold create an angle of sixty degrees?

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.

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.

Angles Inside

Age 11 to 14 Challenge Level:

Draw some angles inside a rectangle. What do you notice? Can you prove it?

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.

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. . . .

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.

Star Polygons

Age 11 to 14 Challenge Level:

Draw some stars and measure the angles at their points. Can you find and prove a result about their sum?

Polygon Pictures

Age 11 to 14 Challenge Level:

Can you work out how these polygon pictures were drawn, and use that to figure out their 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?

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?

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.

Gibraltar Geometry

Age 11 to 14 Challenge Level:

Take a look at the photos of tiles at a school in Gibraltar. What questions can you ask about them?

Tessellating Hexagons

Age 11 to 14 Challenge Level:

Which hexagons tessellate?

Convex Polygons

Age 11 to 14 Challenge Level:

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

Darts and Kites

Age 14 to 16 Challenge Level:

Explore the geometry of these dart and kite shapes!

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?

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

Terminology

Age 14 to 16 Challenge Level:

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

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?

Which Solids Can We Make?

Age 11 to 14 Challenge Level:

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?

Polygon Rings

Age 11 to 14 Challenge Level:

Join pentagons together edge to edge. Will they form a ring?

Getting an Angle

Age 11 to 14 Challenge Level:

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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.

Bow Tie

Age 11 to 14 Challenge Level:

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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.

First Forward Into Logo 9: Stars

Age 11 to 18 Challenge Level:

Turn through bigger angles and draw stars with Logo.