# Resources tagged with: Triangles

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Broad Topics > Angles, Polygons, and Geometrical Proof > Triangles ### Lighting up Time

##### Age 7 to 14 Challenge Level:

A very mathematical light - what can you see? ### 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? ### Squareo'scope Determines the Kind of Triangle

##### Age 11 to 14

A description of some experiments in which you can make discoveries about triangles. ### 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. ### 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. ### 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? ### Ratty

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

If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation? ### Name That Triangle!

##### Age 7 to 11 Challenge Level:

Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know? ### Making Maths: Equilateral Triangle Folding

##### Age 7 to 14 Challenge Level:

Make an equilateral triangle by folding paper and use it to make patterns of your own. ### 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. ### Triangle Transformation

##### Age 7 to 14 Challenge Level:

Start with a triangle. Can you cut it up to make a rectangle? ### Kissing Triangles

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

Determine the total shaded area of the 'kissing triangles'. ### 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? ### Jig Shapes

##### Age 5 to 11 Challenge Level:

Can you each work out what shape you have part of on your card? What will the rest of it look like? ### Triangle Inequality

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

ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm. ### 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? ### 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? ### Part the Polygons

##### Age 7 to 11 Short Challenge Level:

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape. ### 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. ### Folding

##### Age 7 to 11 Challenge Level:

What shapes can you make by folding an A4 piece of paper? ### Sorting Logic Blocks

##### Age 5 to 11 Challenge Level:

This interactivity allows you to sort logic blocks by dragging their images. ### Triangle Island

##### Age 7 to 11 Challenge Level:

You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules? ### Triangle Pin-down

##### Age 7 to 11 Challenge Level:

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs. ### Cut and Make

##### Age 7 to 11 Challenge Level:

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again? ### Egyptian Rope

##### Age 7 to 11 Challenge Level:

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this? ### Bracelets

##### Age 7 to 11 Challenge Level:

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads? ### Rectangle Tangle

##### Age 7 to 11 Challenge Level:

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes? ### Triangles All Around

##### Age 7 to 11 Challenge Level:

Can you find all the different triangles on these peg boards, and find their angles? ### Cut it Out

##### Age 7 to 11 Challenge Level:

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into? ### Making Maths: Test the Strength of a Triangle

##### Age 7 to 11 Challenge Level:

Have you noticed that triangles are used in manmade structures? Perhaps there is a good reason for this? 'Test a Triangle' and see how rigid triangles are. ### Cartesian Isometric

##### Age 7 to 11 Challenge Level:

The graph below is an oblique coordinate system based on 60 degree angles. It was drawn on isometric paper. What kinds of triangles do these points form? ### Transformations on a Pegboard

##### Age 7 to 11 Challenge Level:

How would you move the bands on the pegboard to alter these shapes? ### Peg and Pin Boards

##### Age 5 to 11

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example. ### Shapely Pairs

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

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow... ### Cutting Corners

##### Age 7 to 11 Challenge Level:

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way? ### Folding Flowers 2

##### Age 7 to 11 Challenge Level:

Make a flower design using the same shape made out of different sizes of paper. ### 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? ### Putting Two and Two Together

##### Age 7 to 11 Challenge Level:

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together? ### Cutting it Out

##### Age 5 to 11 Challenge Level:

I cut this square into two different shapes. What can you say about the relationship between them? ### Regular Rings 1

##### Age 7 to 11 Challenge Level:

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes? ### Property Chart

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

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid? ### Isosceles Triangles

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

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw? ### More Transformations on a Pegboard

##### Age 7 to 11 Challenge Level:

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle. ### Triangle Relations

##### Age 7 to 11 Challenge Level:

What do these two triangles have in common? How are they related? ### Nine-pin Triangles

##### Age 7 to 11 Challenge Level:

How many different triangles can you make on a circular pegboard that has nine pegs? ### Notes on a Triangle

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

Can you describe what happens in this film? ### Triangle Shapes

##### Age 5 to 11 Challenge Level:

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them. ### Uncanny Triangles

##### Age 7 to 11 Challenge Level:

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas? ### Tri.'s

##### Age 7 to 11 Challenge Level:

How many triangles can you make on the 3 by 3 pegboard? ### Inside Seven Squares

##### Age 7 to 11 Challenge Level:

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?