Lines Angles And Mathematical Proofs Mastery Test Answers

There are 67 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 16
Challenge Level

How did the the rotation robot make these patterns?

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?

Polygon Rings

Age 11 to 14
Challenge Level

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

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.

Making Sixty

Age 14 to 16
Challenge Level

Why does this fold create an angle of sixty degrees?

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 16
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?

Angles Inside

Age 11 to 14
Challenge Level

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

Shogi Shapes

Age 11 to 14
Challenge 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 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?

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?

Witch's Hat

Age 11 to 16
Challenge Level

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

Cylinder Cutting

Age 7 to 11
Challenge Level

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.

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?

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.

Dotty Circle

Age 7 to 11
Challenge Level

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

Flight Path

Age 16 to 18
Challenge Level

Use simple trigonometry to calculate the distance along the flight path from London to Sydney.

Overlapping Squares

Age 7 to 11
Challenge Level

Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.

Spirostars

Age 16 to 18
Challenge Level

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?

Making Maths: Clinometer

Age 11 to 14
Challenge 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.

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?

Three Tears

Age 14 to 16
Challenge Level

Construct this design using only compasses

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 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.

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.