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#### Resources tagged with Pythagoras' theorem similar to Fit for Photocopying:

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Broad Topics > Pythagoras and Trigonometry > Pythagoras' theorem ### Napkin

##### Age 14 to 16 Challenge Level:

A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed . ### Xtra

##### Age 14 to 18 Challenge Level:

Find the sides of an equilateral triangle ABC where a trapezium BCPQ is drawn with BP=CQ=2 , PQ=1 and AP+AQ=sqrt7 . Note: there are 2 possible interpretations. ### Partly Circles

##### Age 14 to 16 Challenge Level:

What is the same and what is different about these circle questions? What connections can you make? ### Pareq Calc

##### Age 14 to 16 Challenge Level:

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . . ### Matter of Scale

##### Age 14 to 16 Challenge Level:

Prove Pythagoras' Theorem using enlargements and scale factors. ### 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. ### Hex

##### Age 11 to 14 Challenge Level:

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other. ### Tilted Squares

##### Age 11 to 14 Challenge Level:

It's easy to work out the areas of most squares that we meet, but what if they were tilted? ### Square Pegs

##### Age 11 to 14 Challenge Level:

Which is a better fit, a square peg in a round hole or a round peg in a square hole? ### Nicely Similar

##### Age 14 to 16 Challenge Level:

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle? ### Pythagorean Triples I

##### Age 11 to 16

The first of two articles on Pythagorean Triples which asks how many right angled triangles can you find with the lengths of each side exactly a whole number measurement. Try it! ### Pythagoras Proofs

##### Age 14 to 16 Challenge Level:

Can you make sense of these three proofs of Pythagoras' Theorem? ### Pythagorean Triples II

##### Age 11 to 16

This is the second article on right-angled triangles whose edge lengths are whole numbers. ### Picturing Pythagorean Triples

##### Age 14 to 18

This article discusses how every Pythagorean triple (a, b, c) can be illustrated by a square and an L shape within another square. You are invited to find some triples for yourself. ### Some(?) of the Parts

##### Age 14 to 16 Challenge Level:

A circle touches the lines OA, OB and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle ### Floored

##### Age 11 to 14 Challenge Level:

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded? ### Liethagoras' Theorem

##### Age 7 to 14

Liethagoras, Pythagoras' cousin (!), was jealous of Pythagoras and came up with his own theorem. Read this article to find out why other mathematicians laughed at him. ### Garden Shed

##### Age 11 to 14 Challenge Level:

Can you minimise the amount of wood needed to build the roof of my garden shed? ### Fitting In

##### Age 14 to 16 Challenge Level:

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . . ### Squareo'scope Determines the Kind of Triangle

##### Age 11 to 14

A description of some experiments in which you can make discoveries about triangles. ### The Dangerous Ratio

##### Age 11 to 14

This article for pupils and teachers looks at a number that even the great mathematician, Pythagoras, found terrifying. ### Circle Box

##### Age 14 to 16 Challenge Level:

It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit? ### All Tied Up

##### Age 14 to 16 Challenge Level:

A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be? ### Under the Ribbon

##### Age 14 to 16 Challenge Level:

A ribbon is nailed down with a small amount of slack. What is the largest cube that can pass under the ribbon ? ### Compare Areas

##### Age 14 to 16 Challenge Level:

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle? ### Zig Zag

##### Age 14 to 16 Challenge Level:

Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line? ### Isosceles

##### Age 11 to 14 Challenge Level:

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas. ### Semi-detached

##### Age 14 to 16 Challenge Level:

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius. ### Medallions

##### Age 14 to 16 Challenge Level:

Three circular medallions fit in a rectangular box. Can you find the radius of the largest one? ### Pythagorean Triples

##### Age 11 to 14 Challenge Level:

How many right-angled triangles are there with sides that are all integers less than 100 units? ### Tennis

##### Age 11 to 14 Challenge Level:

A tennis ball is served from directly above the baseline (assume the ball travels in a straight line). What is the minimum height that the ball can be hit at to ensure it lands in the service area? ### Rectangular Pyramids

##### Age 14 to 18 Challenge Level:

Is the sum of the squares of two opposite sloping edges of a rectangular based pyramid equal to the sum of the squares of the other two sloping edges? ### Kite in a Square

##### Age 14 to 16 Challenge Level:

Can you make sense of the three methods to work out the area of the kite in the square? ### The Pillar of Chios

##### Age 14 to 16 Challenge Level:

Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle. ### Rhombus in Rectangle

##### Age 14 to 16 Challenge Level:

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus. ### Generating Triples

##### Age 14 to 16 Challenge Level:

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more? ### Take a Square

##### Age 14 to 16 Challenge Level:

Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square. ### All Is Number

##### Age 7 to 14

Read all about Pythagoras' mathematical discoveries in this article written for students. ### Corridors

##### Age 14 to 16 Challenge Level:

A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner. ### Where to Land

##### Age 14 to 16 Challenge Level:

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible? ### Slippage

##### Age 14 to 16 Challenge Level:

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . . ### At a Glance

##### Age 14 to 16 Challenge Level:

The area of a regular pentagon looks about twice as a big as the pentangle star drawn within it. Is it? ### Tilting Triangles

##### Age 14 to 16 Challenge Level:

A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates? ### The Spider and the Fly

##### Age 14 to 16 Challenge Level:

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly? ### Equilateral Areas

##### Age 14 to 16 Challenge Level:

ABC and DEF are equilateral triangles of side 3 and 4 respectively. Construct an equilateral triangle whose area is the sum of the area of ABC and DEF. ### Circle Scaling

##### Age 14 to 16 Challenge Level:

Describe how to construct three circles which have areas in the ratio 1:2:3. ### In a Spin

##### Age 14 to 16 Challenge Level:

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse? ### A Chordingly

##### Age 11 to 14 Challenge Level:

Find the area of the annulus in terms of the length of the chord which is tangent to the inner circle. ### Grid Lockout

##### Age 14 to 16 Challenge Level:

What remainders do you get when square numbers are divided by 4? ### Squaring the Circle and Circling the Square

##### Age 14 to 16 Challenge Level:

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.