# Search by Topic

#### Resources tagged with Angle properties of shapes similar to Pie Cuts:

Filter by: Content type:
Stage:
Challenge level:

### There are 32 results

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

### 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?

### 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.

##### Stage: 3 Challenge Level:

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

### 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?

### Tricircle

##### Stage: 4 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. . . .

### At a Glance

##### Stage: 4 Challenge Level:

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

### Triangles in Circles

##### Stage: 3 Challenge Level:

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

### Convex Polygons

##### Stage: 3 Challenge Level:

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

### 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?

### Polygon Pictures

##### Stage: 3 Challenge Level:

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

##### Stage: 4 Challenge Level:

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?

##### Stage: 4 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?

### 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

### 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.

### Tessellating Hexagons

##### Stage: 3 Challenge Level:

Which hexagons tessellate?

### 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?

### Can You Explain Why?

##### Stage: 3 Challenge Level:

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

### Terminology

##### Stage: 4 Challenge Level:

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

### Getting an Angle

##### Stage: 3 Challenge Level:

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

### Triangles and Petals

##### Stage: 4 Challenge Level:

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

### Bisecting Angles in a Triangle

##### Stage: 3 and 4 Challenge Level:

Measure the two angles. What do you notice?

### 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?

### 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 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.

### A Sameness Surely

##### Stage: 4 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

##### Stage: 4 Challenge Level:

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

### Dodecawhat

##### Stage: 4 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.

### Pentakite

##### Stage: 4 and 5 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

##### Stage: 4 and 5 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.

### First Forward Into Logo 9: Stars

##### Stage: 3, 4 and 5 Challenge Level:

Turn through bigger angles and draw stars with Logo.