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There are **68** NRICH Mathematical resources connected to **Angles - points, lines and parallel lines**, you may find related items under Angles, polygons, and geometrical proof.

Problem
Primary curriculum
Secondary curriculum
### Angles Inside

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polygon Pictures

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangle in a Trapezium

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Isosceles Seven

Is it possible to find the angles in this rather special isosceles triangle?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Polygon Rings

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Same Length

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Olympic Turns

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Which Solids Can We Make?

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Turning

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Six Places to Visit

Can you describe the journey to each of the six places on these maps? How would you turn at each junction?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### How Safe Are You?

How much do you have to turn these dials by in order to unlock the safes?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Round and Round and Round

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Semi-regular Tessellations

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Right Angles

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Subtended Angles

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles in Circles

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Octa-flower

Join some regular octahedra, face touching face and one vertex of each meeting at a point. How many octahedra can you fit around this point?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Watch the Clock

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Angle Trisection

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Quad in Quad

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

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Flexi Quads

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Orbiting Billiard Balls

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Dotty Relationship

Can you draw perpendicular lines without using a protractor? Investigate how this is possible.

Age 7 to 11

Challenge Level

Interactive
Primary curriculum
Secondary curriculum
### Virtual Geoboard

A virtual geoboard that allows you to create shapes by stretching rubber bands between pegs on the board. Allows a variable number of pegs and variable grid geometry and includes a point labeller.

Problem
Primary curriculum
Secondary curriculum
### Pegboard Quads

Make different quadrilaterals on a nine-point pegboard, and work out their angles. What do you notice?

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Angle Measurement: an Opportunity for Equity

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

Age 11 to 16

General
Primary curriculum
Secondary curriculum
### Watch Those Wheels

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sweeping Hands

Use your knowledge of angles to work out how many degrees the hour and minute hands of a clock travel through in different amounts of time.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Right Angle Challenge

How many right angles can you make using two sticks?

Age 5 to 7

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Pythagoras

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.

Age 7 to 14

Article
Primary curriculum
Secondary curriculum
### Coordinates and Descartes

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.

Age 7 to 16

Article
Primary curriculum
Secondary curriculum
### Maurits Cornelius Escher

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 intertwined.

Age 7 to 14

Problem
Primary curriculum
Secondary curriculum
### Flower

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Lunar Angles

What is the sum of the angles of a triangle whose sides are circular arcs on a flat surface? What if the triangle is on the surface of a sphere?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### LOGO Challenge 7 - More Stars and Squares

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

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### LOGO Challenge 8 - Rhombi

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

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### LOGO Challenge 1 - Star Square

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

Age 7 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Take the Right Angle

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Parallel Universe

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Similarly So

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.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Hand Swap

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 minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### On Time

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Arrowhead

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Problem of Time

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Square World

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Clock Hands

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.

Age 7 to 11

Challenge Level