Other tags that relate to Opposite Vertices
Quadrilaterals. Area - triangles, quadrilaterals, compound shapes. Squares. Pythagoras' theorem. Logo. Visualising. 2D shapes and their properties. Circle properties and circle theorems. Regular polygons and circles. Mathematical reasoning & proof.There are 68 results
Broad Topics > Habits of Mind > Curious
Opposite Vertices
Age 11 to 14 Challenge Level:
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
Circles in Quadrilaterals
Age 14 to 16 Challenge Level:
Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.
Trapezium Four
Age 14 to 16 Challenge Level:
The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?
Hexy-metry
Age 14 to 16 Challenge Level:
A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?
Curvy Areas
Age 14 to 16 Challenge Level:
Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
Triangle Midpoints
Age 14 to 16 Challenge Level:
You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?
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?
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?
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?
Blue and White
Age 11 to 14 Challenge Level:
Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?
Triangles and Petals
Age 14 to 16 Challenge Level:
An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?
Perimeter Possibilities
Age 11 to 14 Challenge Level:
I'm thinking of a rectangle with an area of 24. What could its perimeter be?
On the Edge
Age 11 to 14 Challenge Level:
If you move the tiles around, can you make squares with different coloured edges?
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.
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?
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?
Square Coordinates
Age 11 to 14 Challenge Level:
A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
Arclets
Age 14 to 16 Challenge Level:
Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
Vector Journeys
Age 14 to 18 Challenge Level:
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
Partly Painted Cube
Age 14 to 16 Challenge Level:
Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?
Cola Can
Age 11 to 14 Challenge Level:
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
More Number Pyramids
Age 11 to 14 Challenge Level:
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Think of Two Numbers
Age 11 to 14 Challenge Level:
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
Your Number Was...
Age 11 to 14 Challenge Level:
Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?
Take Three from Five
Age 14 to 16 Challenge Level:
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Searching for Mean(ing)
Age 11 to 16 Challenge Level:
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
Cuboid Challenge
Age 11 to 16 Challenge Level:
What's the largest volume of box you can make from a square of paper?
How Much Can We Spend?
Age 11 to 14 Challenge Level:
A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
What Numbers Can We Make?
Age 11 to 14 Challenge Level:
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Charlie's Delightful Machine
Age 11 to 16 Challenge Level:
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Largest Product
Age 11 to 14 Challenge Level:
Which set of numbers that add to 10 have the largest product?
Number Pyramids
Age 11 to 14 Challenge Level:
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Beelines
Age 14 to 16 Challenge Level:
Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?
Fit for Photocopying
Age 14 to 16 Challenge Level:
Explore the relationships between different paper sizes.
Litov's Mean Value Theorem
Age 11 to 14 Challenge Level:
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
Special Numbers
Age 11 to 14 Challenge Level:
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
Summing Consecutive Numbers
Age 11 to 14 Challenge Level:
15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?
Pair Products
Age 14 to 16 Challenge Level:
Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?
What's Possible?
Age 14 to 16 Challenge Level:
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Arithmagons
Age 11 to 16 Challenge Level:
Can you find the values at the vertices when you know the values on the edges?
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?
Multiplication Arithmagons
Age 14 to 16 Challenge Level:
Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?
Elevenses
Age 11 to 14 Challenge Level:
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
What Numbers Can We Make Now?
Age 11 to 14 Challenge Level:
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Statement Snap
Age 7 to 14 Challenge Level:
You'll need to know your number properties to win a game of Statement Snap...
Satisfying Statements
Age 11 to 14 Challenge Level:
Can you find any two-digit numbers that satisfy all of these statements?
Cosy Corner
Age 11 to 14 Challenge Level:
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
A Little Light Thinking
Age 14 to 16 Challenge Level:
Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?
Two's Company
Age 11 to 14 Challenge Level:
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Dicey Operations
Age 11 to 14 Challenge Level:
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
NRICH is part of the family of activities in the Millennium Mathematics Project.