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

At Right Angles

Stage: 3 Challenge Level:

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

Perpendicular Lines

Stage: 3 Challenge Level:

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular 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.

Flexi Quads

Stage: 5 Challenge Level:

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?

Orthogonal Circle

Stage: 5 Challenge Level:

Given any three non intersecting circles in the plane find another circle or straight line which cuts all three circles orthogonally.

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.

Dotty Relationship

Stage: 2 Challenge Level:

Can you draw perpendicular lines without using a protractor? Investigate how this is possible.

Right Angle Challenge

Stage: 1 Challenge Level:

How many right angles can you make using two sticks?

Walls

Stage: 5 Challenge Level:

Plane 1 contains points A, B and C and plane 2 contains points A and B. Find all the points on plane 2 such that the two planes are perpendicular.

A Shade Crossed

Stage: 4 Challenge Level:

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

The Dodecahedron Explained

Stage: 5

What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?

What Are You Plotting?

Stage: 2 Challenge Level:

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

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.

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. . . .

Right Time

Stage: 3 Challenge Level:

At the time of writing the hour and minute hands of my clock are at right angles. How long will it be before they are at right angles again?

Shrink

Stage: 4 Challenge Level:

X is a moveable point on the hypotenuse, and P and Q are the feet of the perpendiculars from X to the sides of a right angled triangle. What position of X makes the length of PQ a minimum?

Quads

Stage: 4 and 5 Challenge Level:

The circumcentres of four triangles are joined to form a quadrilateral. What do you notice about this quadrilateral as the dynamic image changes? Can you prove your conjecture?

Three Way Split

Stage: 4 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.

Square World

Stage: 5 Challenge Level:

P is a point inside a square ABCD such that PA= 1, PB = 2 and PC = 3. How big is angle APB ?