# Resources tagged with: Angles - points, lines and parallel lines

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There are 39 NRICH Mathematical resources connected to Angles - points, lines and parallel lines, you may find related items under Angles, Polygons, and Geometrical Proof.

Broad Topics > Angles, Polygons, and Geometrical Proof > Angles - points, lines and parallel lines

### Robotic Rotations

##### Age 11 to 16Challenge Level

How did the the rotation robot make these patterns?

### Polygon Pictures

##### Age 11 to 14Challenge Level

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

### Polygon Rings

##### Age 11 to 14Challenge Level

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

### Making Sixty

##### Age 14 to 16Challenge Level

Why does this fold create an angle of sixty degrees?

### Round and Round and Round

##### Age 11 to 14Challenge Level

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

### Semi-regular Tessellations

##### Age 11 to 16Challenge Level

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

### Right Angles

##### Age 11 to 14Challenge Level

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

### Subtended Angles

##### Age 11 to 14Challenge 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

##### Age 11 to 14Challenge Level

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

### Estimating Angles

##### Age 7 to 14Challenge Level

How good are you at estimating angles?

### Angle Trisection

##### Age 14 to 16Challenge Level

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

### Quad in Quad

##### Age 14 to 16Challenge Level

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

### Angles Inside

##### Age 11 to 14Challenge Level

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

### Shogi Shapes

##### Age 11 to 14Challenge Level

Shogi tiles can form interesting shapes and patterns... I wonder whether they fit together to make a ring?

### Using Geogebra

##### Age 11 to 18

Never used GeoGebra before? This article for complete beginners will help you to get started with this free dynamic geometry software.

### Triangle in a Trapezium

##### Age 11 to 16Challenge Level

Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?

### Same Length

##### Age 11 to 16Challenge Level

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

### Witch's Hat

##### Age 11 to 16Challenge Level

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

### Which Solids Can We Make?

##### Age 11 to 14Challenge 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?

### Interacting with the Geometry of the Circle

##### Age 5 to 16

Jennifer Piggott and Charlie Gilderdale describe a free interactive circular geoboard environment that can lead learners to pose mathematical questions.

### Making Maths: Clinometer

##### Age 11 to 14Challenge Level

You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, Make a clinometer and use it to help you estimate the heights of tall objects.

### Making Maths: Equilateral Triangle Folding

##### Age 7 to 14Challenge Level

Make an equilateral triangle by folding paper and use it to make patterns of your own.

### Tessellating Hexagons

##### Age 11 to 14Challenge Level

Which hexagons tessellate?

### Orbiting Billiard Balls

##### Age 14 to 16Challenge Level

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

### Three Tears

##### Age 14 to 16Challenge Level

Construct this design using only compasses

### Pegboard Quads

##### Age 14 to 16Challenge 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?

### Angle Measurement: an Opportunity for Equity

##### Age 11 to 16

Suggestions for worthwhile mathematical activity on the subject of angle measurement for all pupils.

### Pythagoras

##### Age 7 to 14

Pythagoras of Samos was a Greek philosopher who lived from about 580 BC to about 500 BC. Find out about the important developments he made in mathematics, astronomy, and the theory of music.

### Coordinates and Descartes

##### Age 7 to 16

Have you ever wondered how maps are made? Or perhaps who first thought of the idea of designing maps? We're here to answer these questions for you.

### Maurits Cornelius Escher

##### Age 7 to 14

Have you ever noticed how mathematical ideas are often used in patterns that we see all around us? This article describes the life of Escher who was a passionate believer that maths and art can be. . . .

### LOGO Challenge 7 - More Stars and Squares

##### Age 11 to 16Challenge Level

Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

### LOGO Challenge 8 - Rhombi

##### Age 7 to 16Challenge Level

Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?

### LOGO Challenge 1 - Star Square

##### Age 7 to 16Challenge Level

Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.

### Parallel Universe

##### Age 14 to 16Challenge Level

An equilateral triangle is constructed on BC. A line QD is drawn, where Q is the midpoint of AC. Prove that AB // QD.

### Similarly So

##### Age 14 to 16Challenge Level

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

### Hand Swap

##### Age 14 to 16Challenge Level

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .

### On Time

##### Age 11 to 14Challenge Level

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

### Arrowhead

##### Age 14 to 16Challenge Level

The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?

### A Problem of Time

##### Age 14 to 16Challenge Level

Consider a watch face which has identical hands and identical marks for the hours. It is opposite to a mirror. When is the time as read direct and in the mirror exactly the same between 6 and 7?