Resources tagged with: Triangles

Filter by: Content type:
Age range:
Challenge level:

There are 42 results

Broad Topics > Angles, Polygons, and Geometrical Proof > Triangles

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.

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.

Wedge on Wedge

Age 14 to 16
Challenge Level

Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?

Arrh!

Age 14 to 16
Challenge Level

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. . . .

Three Way Split

Age 14 to 16
Challenge Level

Take any point P inside an equilateral triangle. Draw PA, PB and PC from P perpendicular to the sides of the triangle where A, B and C are points on the sides. Prove that PA + PB + PC is a constant.

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?

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.

Floored

Age 14 to 16
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?

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?

Equal Equilateral Triangles

Age 14 to 16
Challenge Level

Can you make a regular hexagon from yellow triangles the same size as a regular hexagon made from green triangles ?

Tricircle

Age 14 to 16
Challenge Level

The centre of the larger circle is at the midpoint of one side of an equilateral triangle and the circle touches the other two sides of the triangle. A smaller circle touches the larger circle and. . . .

The Square Hole

Age 14 to 16
Challenge Level

If the yellow equilateral triangle is taken as the unit for area, what size is the hole ?

A Shade Crossed

Age 14 to 16
Challenge Level

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

Squareo'scope Determines the Kind of Triangle

Age 11 to 14

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

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. . . .

Circumnavigation

Age 14 to 16
Challenge Level

The sides of a triangle are 25, 39 and 40 units of length. Find the diameter of the circumscribed circle.

Half a Triangle

Age 14 to 16
Challenge Level

Construct a line parallel to one side of a triangle so that the triangle is divided into two equal areas.

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.

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.

Triangle in a Triangle

Age 14 to 16
Challenge Level

Can you work out the fraction of the original triangle that is covered by the inner triangle?

Lighting up Time

Age 7 to 14
Challenge Level

A very mathematical light - what can you see?

Farhan's Poor Square

Age 14 to 16
Challenge Level

From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.

Kissing Triangles

Age 11 to 14
Challenge Level

Determine the total shaded area of the 'kissing triangles'.

Are You Kidding

Age 14 to 16
Challenge Level

If the altitude of an isosceles triangle is 8 units and the perimeter of the triangle is 32 units.... What is the area of the triangle?

LOGO Challenge 5 - Patch

Age 11 to 16
Challenge Level

Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

Triangle Transformation

Age 7 to 14
Challenge Level

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

Two Triangles in a Square

Age 14 to 16
Challenge Level

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.

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?

Pareq Exists

Age 14 to 16
Challenge Level

Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.

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?

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.

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...

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?

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?

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.

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?

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. . . .

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?

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?

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?

Notes on a Triangle

Age 11 to 14
Challenge Level

Can you describe what happens in this film?

Calculating with Cosines

Age 14 to 18
Challenge Level

If I tell you two sides of a right-angled triangle, you can easily work out the third. But what if the angle between the two sides is not a right angle?