26 154 201 Construct a triangle PQR with lines PQ 8cm QR 5cm and PQR 40 Draw an 8cm line and label the ends P and Q This is the line PQ Place the centre of the protractor on Q with the 0 line pointing to P ID: 929794
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Slide1
Starter
Using a protractor, draw the angles:
26°
154°
201°
Slide2Construct a triangle PQR with lines PQ = 8cm, QR = 5cm and PQR = 40°
Draw an 8cm line and label the ends P and Q. This is the line PQ. Place the centre of the protractor on Q with the 0° line pointing to P.
Measure a 40° angle clockwise from 0°. Mark it with a dot. Draw a 5cm line from Q through the dot. Label the end of this line R. Join up P and R to complete the triangle.
P
Q
.
R
40
°
8cm
5cm
Slide3P
Q
Draw an 8cm line and label the ends P and Q. This is the line PQ.
Place the centre of the protractor on Q with the 0° line pointing to P. Measure a 40° angle clockwise from 0°. Mark it with a dot. Draw a line from Q through the dot. Place the centre of the protractor on P with the 0° line pointing to Q. Measure a 30° angle anticlockwise from 0°. Complete as with other angle. Point R is where the two lines meet.
.
R
40
°
8cm
.
30
°
Construct a triangle PQR with lines PQ = 8cm,
PQR = 40
° and
RPQ = 30
°
Slide4A
B
C
Construct a triangle ABC with side lengths AB = 9cm, AC = 5cm and BC = 7cm.
Draw a 9cm line and label the ends A and B. This is the line AB.
Set your compasses to 5cm and with the point on A draw an arc.
Set your compasses to 7cm and with the point on B draw an arc.
Label this point C and join A to C then B to C to get the lines AC and BC.
9cm
5cm
7cm
Slide5Plenary
Accurately construct the quadrilateral using the given information
6cm
5cm
2cm
100°
120°
How long is the top side of the quadrilateral?
Slide6StarterA
AB
A
B
Draw a circle and mark a point A on its circumference.
Keep the compasses set at the size of the radius, and from point A draw an arc that cuts the circle at point B.
Repeat the process until six point are marked on the circumference. Join the points to make a regular hexagon.
Slide7A Locus is the path you would follow if you were given certain instructions.
“Loci” is the plural of “Locus”.
Eg. You must walk so that you are always 5 metres inside the fence surrounding the school fields. Where must you walk?
Eg. A goat is tethered to a rope that is 4 metres long. Show the region the goat can reach.Loci
Slide8There are only FOUR loci.
(1) A fixed distance from a fixed point.
(2) A fixed distance from a fixed line.(4) The same distance from two fixed lines.
Lets look at the four loci individually
(3) The same distance from two fixed points.Loci
Slide9A fixed distance from a fixed point
We end up with a circle of radius r
r
Slide10We end up with parallel lines.
But what about at the ends?
A fixed distance from a fixed line
Slide11The same distance from two fixed points
Step 1 Open a pair of compasses to a distance that is slightly greater than half the distance between the points.
Step 2 From one point draw two arcs, one above the points and one below.
Step 3 Repeat this from the other point.
Step 4 Join where the arcs cross together.
Slide12The same distance from two fixed lines
Step 1 On each line draw an arc, centred at the point where the lines cross.
Step 2 From each of these points draw two more arcs.
Step 3 Join where the arcs cross to where the lines cross.
Slide13The map above, drawn to a scale of 4cm to 1 km, shows the positions of three villages, Layton, Moorby and Newdon.Simon’s house is the same distance from Moorby as it is from Layton. The house is also less than ¾ km from Newdon.Mark on the map the possible positions of Simon’s house. Show your construction lines clearly.
Moorby Newdon
Layton