Resources tagged with: Angle properties of polygons

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There are 44 NRICH Mathematical resources connected to Angle properties of polygons, you may find related items under Angles, Polygons, and Geometrical Proof.

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

Always, Sometimes or Never? Shape

Age 7 to 11
Challenge Level

Are these statements always true, sometimes true or never true?

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?

Polygon Rings

Age 11 to 14
Challenge Level

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

Walking Round a Triangle

Age 5 to 7
Challenge Level

This ladybird is taking a walk round a triangle. Can you see how much he has turned when he gets back to where he started?

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?

Making Sixty

Age 14 to 16
Challenge Level

Why does this fold create an angle of sixty degrees?

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?

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?

Terminology

Age 14 to 16
Challenge Level

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

Transformations on a Pegboard

Age 7 to 11
Challenge Level

How would you move the bands on the pegboard to alter these shapes?

Data Duos

Age 7 to 11
Challenge Level

Can you match the Venn diagram with the Carroll diagram that shows the same information?

Possible Pairs

Age 7 to 11
Challenge Level

In this game, you turn over two cards and try to draw a triangle which has both properties.

Name That Triangle!

Age 7 to 11
Challenge Level

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?

Triangle or No Triangle?

Age 5 to 7
Challenge Level

Here is a selection of different shapes. Can you work out which ones are triangles, and why?

Angles Inside

Age 11 to 14
Challenge Level

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

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?

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?

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?

Road Maker 2

Age 16 to 18 Short
Challenge Level

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

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.

Tessellating Hexagons

Age 11 to 14
Challenge Level

Which hexagons tessellate?

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?

Triangle Pin-down

Age 7 to 11
Challenge Level

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Triangles All Around

Age 7 to 11
Challenge Level

Can you find all the different triangles on these peg boards, and find their angles?

Cartesian Isometric

Age 7 to 11
Challenge Level

The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form?

Fred the Class Robot

Age 7 to 11
Challenge Level

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

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.

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.

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.

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.

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.

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?

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.

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. . . .

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?

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

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.

Darts and Kites

Age 14 to 16
Challenge Level

Explore the geometry of these dart and kite shapes!

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.

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?