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Resources tagged with Angle properties of shapes similar to Lighting up Time:

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Broad Topics > 2D Geometry, Shape and Space > Angle properties of shapes

Angle A

Stage: 3 Challenge Level:

The three corners of a triangle are sitting on a circle. The angles are called Angle A, Angle B and Angle C. The dot in the middle of the circle shows the centre. The counter is measuring the size. . . .

Arclets Explained

Stage: 3 and 4

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.

Pie Cuts

Stage: 3 Challenge Level:

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

Floored

Stage: 3 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?

Polygon Pictures

Stage: 3 Challenge Level:

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

Fred the Class Robot

Stage: 2 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?

Star Polygons

Stage: 3 Challenge Level:

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

Convex Polygons

Stage: 3 Challenge Level:

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

Stage: 3 Challenge Level:

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

Getting an Angle

Stage: 3 Challenge Level:

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

Can You Explain Why?

Stage: 3 Challenge Level:

Can you explain why it is impossible to construct this triangle?

Tessellating Hexagons

Stage: 3 Challenge Level:

Which hexagons tessellate?

Triangle Pin-down

Stage: 2 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

Stage: 2 Challenge Level:

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

Cartesian Isometric

Stage: 2 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?

Bisecting Angles in a Triangle

Stage: 3 and 4 Challenge Level:

Measure the two angles. What do you notice?

Subtended Angles

Stage: 3 Challenge Level:

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

Triangles in Circles

Stage: 3 Challenge Level:

Can you find triangles on a 9-point circle? Can you work out their angles?

Transformations on a Pegboard

Stage: 2 Challenge Level:

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

Semi-regular Tessellations

Stage: 3 Challenge Level:

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

Always, Sometimes or Never? Shape

Stage: 2 Challenge Level:

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

Angles in Three Squares

Stage: 3 and 4 Challenge Level:

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

First Forward Into Logo 9: Stars

Stage: 3, 4 and 5 Challenge Level:

Turn through bigger angles and draw stars with Logo.

First Forward Into Logo 7: Angles of Polygons

Stage: 3, 4 and 5 Challenge Level:

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

LOGO Challenge 4 - Squares to Procedures

Stage: 3 and 4 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

Stage: 2, 3 and 4 Challenge Level:

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

Which Solids Can We Make?

Stage: 3 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?