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Constructions

Use a ruler and compasses to construct lines and angles accurately.
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This is level 2: Perpendicular through a point on a line. Give your answers in centimetres to one decimal place. Score at least 3 correct answers to earn a trophy. Your measurements can be up to 2 mm from the correct value and still be marked correct and you do this activity online.

1

Draw a horizontal line segment PQ 9.3 cm long near the top of your page.

Mark the point S on PQ such that PS is 3cm.

Construct the perpendicular to PQ which passes through S.

Mark a point R on this perpendicular that is 5 cm below S.

Measure the length of QR.

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2

A straight footpath AB is 12.5 cm long on a scale drawing.

Draw a vertical line segment AB 12.5 cm long.

Mark a point T on AB such that AT is 6 cm.

A hedge is to be planted at right angles to the footpath.

Construct the perpendicular to AB through T.

Mark a point H on this perpendicular that is 5 cm to the right of T.

Measure the distance from B to H.

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3

A harbour wall LM is shown on a scale drawing.

Draw a vertical line segment LM 11.8 cm long.

Mark a point S on LM such that SM is 5 cm.

A floating pontoon extends at right angles from the wall.

Construct the perpendicular to LM through S.

Mark a point F on this perpendicular that is 9 cm to the left of S.

Measure the distance from L to F.

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4

Here is a very useful diagram, first studied by Euclid and later popularised by René Descartes.

Draw a horizontal line segment AB, 9 cm long.

Extend AB to the right to a point C, so that BC is 1 cm.

Using AC as the diameter, construct a semicircle above the line AC.

At the point B, construct the perpendicular to AC. This perpendicular meets the curved edge of the semicircle at D.

Measure the length of BD.

Afterwards, try to figure out why this diagram is particularly useful.

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Check

Can you correct your mistakes in order to get full marks?

This is Constructions level 2. You can also try:
Level 1 Level 3 Level 4 Level 5

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.
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Description of Levels

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Level 1 - Perpendicular bisector

Level 2 - Perpendicular through a point on a line

Level 3 - Perpendicular from a point outside a line

Level 4 - Construct triangles and angle bisectors

Level 5 - Construct triangles and standard-angles

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

Loci - including lesson Starters, visual aids and investigations.

Scale Drawings - Use the online tools to measure and construct scale drawings.

Pairs - Match the description of the loci to the diagram of the construction

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Help

 

Step-by-step instructions for drawing the perpendicular from a point on the line.

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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