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Broad Topics > 2D Geometry, Shape and Space > Parallel lines

### Making Sixty

##### Stage: 4 Challenge Level:

Why does this fold create an angle of sixty degrees?

### Parallel Lines

##### Stage: 3 Challenge Level:

How does the position of the line affect the equation of the line? What can you say about the equations of parallel lines?

### Angle Trisection

##### Stage: 4 Challenge Level:

It is impossible to trisect an angle using only ruler and compasses but it can be done using a carpenter's square.

### Sorting Letters

##### Stage: 1 and 2 Challenge Level:

This interactivity allows you to sort letters of the alphabet into two groups according to different properties.

### Floating in Space

##### Stage: 4 Challenge Level:

Two angles ABC and PQR are floating in a box so that AB//PQ and BC//QR. Prove that the two angles are equal.

### What Are You Plotting?

##### Stage: 2 Challenge Level:

Investigate the positions of points which have particular x and y coordinates. What do you notice?

### Parallel Universe

##### Stage: 4 Challenge Level:

An equilateral triangle is constructed on BC. A line QD is drawn, where Q is the midpoint of AC. Prove that AB // QD.

### Similarly So

##### Stage: 4 Challenge Level:

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

### Bi-cyclics

##### Stage: 4 Challenge Level:

Two circles intersect at A and B. Points C and D move round one circle. CA and DB cut the other circle at E and F. What do you notice about the line segments CD and EF?

### On Time

##### Stage: 3 Challenge Level:

On a clock the three hands - the second, minute and hour hands - are on the same axis. How often in a 24 hour day will the second hand be parallel to either of the two other hands?

### Lawnmower

##### Stage: 4 Challenge Level:

A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of. . . .