Other tags that relate to Two Triangles in a Square
Similarity and congruence. Rotations. Reflections. Pythagoras' theorem. Symmetry. Visualising. Ratio and proportion. Triangles. Mathematical reasoning & proof. Squares.There are 179 results
Broad Topics > Thinking Mathematically > Visualising
Triangular Tantaliser
Age 11 to 14
Challenge Level
Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.
Trice
Age 11 to 14
Challenge Level
ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?
Reflecting Squarely
Age 11 to 14
Challenge Level
In how many ways can you fit all three pieces together to make shapes with line symmetry?
Shady Symmetry
Age 11 to 14
Challenge Level
How many different symmetrical shapes can you make by shading triangles or squares?
Star Gazing
Age 14 to 16
Challenge Level
Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.
Concrete Wheel
Age 11 to 14
Challenge Level
A huge wheel is rolling past your window. What do you see?
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?
Zooming in on the Squares
Age 7 to 14
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
Coloured Edges
Age 11 to 14
Challenge Level
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
Dotty Triangles
Age 11 to 14
Challenge Level
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
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.
Tetra Square
Age 11 to 14
Challenge Level
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
Framed
Age 11 to 14
Challenge Level
Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .
Rati-o
Age 11 to 14
Challenge Level
Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?
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. . . .
Weighty Problem
Age 11 to 14
Challenge Level
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
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?
On the Edge
Age 11 to 14
Challenge Level
If you move the tiles around, can you make squares with different coloured edges?
Square It
Age 11 to 16
Challenge Level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
Something in Common
Age 14 to 16
Challenge Level
A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
Ten Hidden Squares
Age 7 to 14
Challenge Level
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
LOGO Challenge - Circles as Animals
Age 11 to 16
Challenge Level
See if you can anticipate successive 'generations' of the two animals shown here.
Eight Hidden Squares
Age 7 to 14
Challenge Level
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Baravelle
Age 7 to 16
Challenge Level
What can you see? What do you notice? What questions can you ask?
Constructing Triangles
Age 11 to 14
Challenge Level
Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?
Natural Sum
Age 14 to 16
Challenge Level
The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .
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. . . .
A Problem of Time
Age 14 to 16
Challenge 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?
Counting Triangles
Age 11 to 14
Challenge Level
Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
Coke Machine
Age 14 to 16
Challenge Level
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
Dissect
Age 11 to 14
Challenge Level
What is the minimum number of squares a 13 by 13 square can be dissected into?
Just Opposite
Age 14 to 16
Challenge Level
A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
Prime Magic
Age 7 to 16
Challenge Level
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
Rolling Around
Age 11 to 14
Challenge Level
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
Rolling Triangle
Age 11 to 14
Challenge Level
The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.
Chess
Age 11 to 14
Challenge Level
What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?
Linkage
Age 11 to 14
Challenge Level
Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?
Take Ten
Age 11 to 14
Challenge Level
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
Tourism
Age 11 to 14
Challenge Level
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
John's Train Is on Time
Age 11 to 14
Challenge Level
A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?
Thinking Through, and By, Visualising
Age 7 to 16
This article is based on some of the ideas that emerged during the production of a book which takes visualising as its focus. We began to identify problems which helped us to take a structured view. . . .
Soma - So Good
Age 11 to 14
Challenge Level
Can you mentally fit the 7 SOMA pieces together to make a cube? Can you do it in more than one way?
Squares, Squares and More Squares
Age 11 to 14
Challenge Level
Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
Playground Snapshot
Age 7 to 14
Challenge Level
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
Cutting a Cube
Age 11 to 14
Challenge Level
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
Tetrahedra Tester
Age 11 to 14
Challenge Level
An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?
Wari
Age 14 to 16
Challenge Level
This is a simple version of an ancient game played all over the world. It is also called Mancala. What tactics will increase your chances of winning?
NRICH is part of the family of activities in the Millennium Mathematics Project.