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Resources tagged with Similarity similar to Mean Geometrically:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Transformations and their Properties > Similarity

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Triangles in a Square

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Plex

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

Plex lets you specify a mapping between points and their images. Then you can draw and see the transformed image.

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Squirty

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.

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Figure of Eight

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

On a nine-point pegboard a band is stretched over 4 pegs in a "figure of 8" arrangement. How many different "figure of 8" arrangements can be made ?

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Von Koch Curve

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.

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Fit for Photocopying

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Photocopiers can reduce from A3 to A4 without distorting the image. Explore the relationships between different paper sizes that make this possible.

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From All Corners

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Straight lines are drawn from each corner of a square to the mid points of the opposite sides. Express the area of the octagon that is formed at the centre as a fraction of the area of the square.

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Squareflake

Stage: 5 Challenge Level: Challenge Level:1

A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.

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Strange Rectangle

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.

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Two Ladders

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Two ladders are propped up against facing walls. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second. . . .

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Look Before You Leap

Stage: 4 Challenge Level: Challenge Level:1

The diagonals of a square meet at O. The bisector of angle OAB meets BO and BC at N and P respectively. The length of NO is 24. How long is PC?

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Napkin

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .

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The Eyeball Theorem

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Two tangents are drawn to the other circle from the centres of a pair of circles. What can you say about the chords cut off by these tangents. Be patient - this problem may be slow to load.

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Golden Triangle

Stage: 5 Challenge Level: Challenge Level:1

Three triangles ABC, CBD and ABD (where D is a point on AC) are all isosceles. Find all the angles. Prove that the ratio of AB to BC is equal to the golden ratio.

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Pentabuild

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Explain how to construct a regular pentagon accurately using a straight edge and compass.

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Sierpinski Triangle

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.

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Matter of Scale

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Prove Pythagoras Theorem using enlargements and scale factors.

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Flower

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Six circles around a central circle make a flower. Watch the flower as you change the radii in this circle packing. Prove that with the given ratios of the radii the petals touch and fit perfectly.

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Chord

Stage: 5 Challenge Level: Challenge Level:1

Equal touching circles have centres on a line. From a point of this line on a circle, a tangent is drawn to the farthest circle. Find the lengths of chords where the line cuts the other circles.

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Quad in Quad

Stage: 4 Challenge Level: Challenge Level:1

The points P, Q, R and S are the midpoints of the edges of a convex quadrilateral. What do you notice about the quadrilateral PQRS as the convex quadrilateral changes?

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A Shade Crossed

Stage: 4 Challenge Level: Challenge Level:1

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

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Fitting In

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

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Take a Square II

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

What fractions can you divide the diagonal of a square into by simple folding?

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Nicely Similar

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Sitting Pretty

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Chords

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Two intersecting circles have a common chord AB. The point C moves on the circumference of the circle C1. The straight lines CA and CB meet the circle C2 at E and F respectively. As the point C. . . .

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Folding Squares

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The diagonal of a square intersects the line joining one of the unused corners to the midpoint of the opposite side. What do you notice about the line segments produced?

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All Tied Up

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Bus Stop

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

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Slippage

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

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Pent

Stage: 4 and 5 Challenge Level: Challenge Level:2 Challenge Level:2

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.