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.
Broad Topics > Angles, Polygons, and Geometrical Proof > Angles - points, lines and parallel lines
Angles Inside
Age 11 to 14
Challenge Level
Draw some angles inside a rectangle. What do you notice? Can you prove it?
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?
Triangle in a Trapezium
Age 11 to 16
Challenge Level
Can you find and prove the relationship between the area of a trapezium and the area of a triangle constructed within it?
Isosceles Seven
Age 14 to 16
Challenge Level
Is it possible to find the angles in this rather special isosceles triangle?
Polygon Rings
Age 11 to 14
Challenge Level
Join pentagons together edge to edge. Will they form a ring?
Same Length
Age 11 to 16
Challenge Level
Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?
Olympic Turns
Age 7 to 11
Challenge Level
This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.
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?
Turning
Age 5 to 7
Challenge Level
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
Six Places to Visit
Age 7 to 11
Challenge Level
Can you describe the journey to each of the six places on these maps? How would you turn at each junction?
How Safe Are You?
Age 7 to 11
Challenge Level
How much do you have to turn these dials by in order to unlock the safes?
Round and Round and Round
Age 11 to 14
Challenge 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 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?
Right Angles
Age 11 to 14
Challenge 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 14
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
Age 11 to 14
Challenge Level
Can you find triangles on a 9-point circle? Can you work out their angles?
Octa-flower
Age 16 to 18
Challenge Level
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?
Watch the Clock
Age 7 to 11
Challenge Level
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?
Angle Trisection
Age 14 to 16
Challenge 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 18
Challenge Level
Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
Flexi Quads
Age 16 to 18
Challenge Level
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?
Orbiting Billiard Balls
Age 14 to 16
Challenge Level
What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?
Dotty Relationship
Age 7 to 11
Challenge Level
Can you draw perpendicular lines without using a protractor? Investigate how this is possible.
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.
Pegboard Quads
Age 14 to 16
Challenge Level
Make different quadrilaterals on a nine-point pegboard, and work out their angles. What do you notice?
Angle Measurement: an Opportunity for Equity
Age 11 to 16
Suggestions for worthwhile mathematical activity on the subject of angle measurement for all pupils.
Watch Those Wheels
Age 5 to 7
Challenge Level
Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!
Sweeping Hands
Age 7 to 11
Challenge Level
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.
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 intertwined.
Flower
Age 16 to 18
Challenge Level
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.
Lunar Angles
Age 16 to 18
Challenge Level
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?
LOGO Challenge 7 - More Stars and Squares
Age 11 to 16
Challenge 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 16
Challenge Level
Explore patterns based on a rhombus. How can you enlarge the pattern - or explode it?
LOGO Challenge 1 - Star Square
Age 7 to 16
Challenge Level
Can you use LOGO to create this star pattern made from squares. Only basic LOGO knowledge needed.
Take the Right Angle
Age 7 to 11
Challenge Level
How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.
Parallel Universe
Age 14 to 16
Challenge 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 16
Challenge 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 16
Challenge 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 minute hand and hour hand had swopped places. What time did the train leave London and how long did the journey take?
On Time
Age 11 to 14
Challenge 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 16
Challenge 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 16
Challenge 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?
Square World
Age 16 to 18
Challenge Level
P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?
Clock Hands
Age 7 to 11
Challenge Level
This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.
NRICH is part of the family of activities in the Millennium Mathematics Project.