Other tags that relate to Handy Angles
2D shapes and their properties. Area - squares and rectangles. Regular polygons and circles. Circumference and arc length. Creating and manipulating expressions and formulae. Mathematical reasoning & proof. Visualising. Circle properties and circle theorems. Pythagoras' theorem. Area - circles, sectors and segments.There are 131 results
Broad Topics > Algebraic expressions, equations and formulae > Creating and manipulating expressions and formulae
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.
Salinon
Age 14 to 16
Challenge Level
This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?
Three Four Five
Age 14 to 16
Challenge Level
Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.
Gutter
Age 14 to 16
Challenge Level
Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?
Sitting Pretty
Age 14 to 16
Challenge Level
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
Semi-square
Age 14 to 16
Challenge Level
What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
Lens Angle
Age 14 to 16
Challenge Level
Find the missing angle between the two secants to the circle when the two angles at the centre subtended by the arcs created by the intersections of the secants and the circle are 50 and 120 degrees.
The Medieval Octagon
Age 14 to 16
Challenge Level
Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.
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?
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. . . .
Can They Be Equal?
Age 11 to 14
Challenge Level
Can you find rectangles where the value of the area is the same as the value of the perimeter?
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?
Pythagoras Proofs
Age 14 to 16
Challenge Level
Can you make sense of these three proofs of Pythagoras' Theorem?
Terminology
Age 14 to 16
Challenge Level
Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?
More Mathematical Mysteries
Age 11 to 14
Challenge Level
Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .
Square Pizza
Age 14 to 16
Challenge Level
Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
A Tilted Square
Age 14 to 16
Challenge Level
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Areas of Parallelograms
Age 14 to 16
Challenge Level
Can you find the area of a parallelogram defined by two vectors?
Perimeter Expressions
Age 11 to 14
Challenge Level
Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?
Difference of Two Squares
Age 14 to 16
Challenge Level
What is special about the difference between squares of numbers adjacent to multiples of three?
Robert's Spreadsheet
Age 14 to 16
Challenge Level
Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?
Square Number Surprises
Age 14 to 16
Challenge Level
There are unexpected discoveries to be made about square numbers...
Always the Same
Age 11 to 14
Challenge Level
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
Multiplication Square
Age 14 to 16
Challenge Level
Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?
Quadratic Patterns
Age 11 to 14
Challenge Level
Surprising numerical patterns can be explained using algebra and diagrams...
Pick's Theorem
Age 14 to 16
Challenge Level
Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.
One and Three
Age 14 to 16
Challenge Level
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
Training Schedule
Age 14 to 16
Challenge Level
The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?
How Big?
Age 11 to 14
Challenge Level
If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?
Puzzling Place Value
Age 14 to 16
Challenge Level
Can you explain what is going on in these puzzling number tricks?
Your Number Is...
Age 7 to 14
Challenge Level
Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
Marbles in a Box
Age 11 to 16
Challenge Level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
Algebra Match
Age 11 to 16
Challenge Level
A task which depends on members of the group noticing the needs of others and responding.
Screen Shot
Age 14 to 16
Challenge Level
A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .
Algebra from Geometry
Age 11 to 16
Challenge Level
Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.
Pythagoras Perimeters
Age 14 to 16
Challenge Level
If you know the perimeter of a right angled triangle, what can you say about the area?
Pinned Squares
Age 14 to 16
Challenge Level
What is the total number of squares that can be made on a 5 by 5 geoboard?
Is it Magic or Is it Maths?
Age 11 to 14
Challenge Level
Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . .
Good Work If You Can Get It
Age 11 to 14
Challenge Level
A job needs three men but in fact six people do it. When it is finished they are all paid the same. How much was paid in total, and much does each man get if the money is shared as Fred suggests?
Diophantine N-tuples
Age 14 to 16
Challenge Level
Can you explain why a sequence of operations always gives you perfect squares?
Mindreader
Age 11 to 14
Challenge Level
A little bit of algebra explains this 'magic'. Ask a friend to pick 3 consecutive numbers and to tell you a multiple of 3. Then ask them to add the four numbers and multiply by 67, and to tell you. . . .
Boxed In
Age 11 to 14
Challenge Level
A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?
Around and Back
Age 14 to 16
Challenge Level
A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .
Dating Made Easier
Age 14 to 16
Challenge Level
If a sum invested gains 10% each year how long before it has doubled its value?
Never Prime
Age 14 to 16
Challenge Level
If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.
Janine's Conjecture
Age 14 to 16
Challenge Level
Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .
Cubes Within Cubes Revisited
Age 11 to 14
Challenge Level
Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?
NRICH is part of the family of activities in the Millennium Mathematics Project.