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

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

Age 14 to 16Challenge Level

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

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?

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?

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.

Making Sixty

Age 14 to 16Challenge Level

Why does this fold create an angle of sixty degrees?

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.

Angles Inside

Age 11 to 14Challenge Level

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

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?

Three Tears

Age 14 to 16Challenge Level

Construct this design using only compasses

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?

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.

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?

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?

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.

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?

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?

Triangles in Circles

Age 11 to 14Challenge Level

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

Polygon Rings

Age 11 to 14Challenge Level

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

Robotic Rotations

Age 11 to 16Challenge Level

How did the the rotation robot make these patterns?

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.

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.

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?

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?

Angle Measurement: an Opportunity for Equity

Age 11 to 16

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

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?

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. . . .

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.

Tessellating Hexagons

Age 11 to 14Challenge Level

Which hexagons tessellate?

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?

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?

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.

Estimating Angles

Age 7 to 14Challenge Level

How good are you at estimating angles?

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?

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.

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?

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?

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.