The Sieve of Eratosthenes - E

GR 9 3-5-7-2 LEARNERS
Page 1 of 4
NAME:
Gr 9
Date:
Time
1 hr.
3-5 Construction of Geometric Figures Investigate sides, angles
CAPS
and diagonals in quadrilaterals, focusing on the diagonals of
Reference
rectangles, squares, parallelograms, rhombi and kite
3-5-7/2 Investigate diagonals in quadrilaterals.
Topic
1.
Think First! [5 mins]
What do you know about the diagonals of your shapes?
Is it possible to construct certain quadrilaterals using facts about their diagonals?
Once you have done this, you can complete the table about properties of quadrilaterals which
you started on the previous worksheet.
If you are unable to do 1 above, do the following exercise which will help you to complete the
table.
2.
Go ahead! [50 mins]
NEW FACTS ABOUT QUADRILATERALS
2.1
Q
SQUARE
M
P
R
S
2.1.1 Draw a line segment PR exactly 10 cm.
2.1.2 Construct the perpendicular bisector of this line segment, naming the point of
intersection M.
2.1.3 Mark off MQ and MS = 5 cm on the perpendicular bisector.
2.1.4 Join PQGS.
2.1.5 Measure the sides and angles to verify you have drawn a square.
2.1.6 What do you know about the diagonals from your construction?
2.1.7 Write the new facts you have learnt about a square on your table.
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GR 9 3-5-7-2 LEARNERS
2.2
Page 2 of 4
RECTANGLE
C
D
B
V
A
2.2.1
2.2.2
2.2.3
2.2.4
2.2.5
2.2.6
Construct an angle of 60°. Name the vertex V.
Extend the arms of the angle to make a pair of vertically opposite angles.
From V mark off VA VB VC VD = 4 cm.
Join ABCD.
What kind of quadrilateral is ABCD? Check the sides and angles to help you.
Write the new facts you have learnt about a rectangle on your table.
2.3
RHOMBUS
N
L
M
P
2.3.1 Construct an isosceles triangle with equal sides LN and MN 6 cm
and the third side DG 5 cm.
2.3.2 Construct a second isosceles triangle LPM with LP = MP = 6 cm,
and LM the base of the first isosceles triangle.
2.3.3 Construct the perpendicular bisector of LM
2.3.4 What happens?
2.3.5 Measure each of the angles of the rhombus. What do you notice?
2.3.6 Write all the facts you have discovered about a rhombus on the table.
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www.e-classroom.co.za
GR 9 3-5-7-2 LEARNERS
2.4
Page 3 of 4
PARALLELOGRAM
Q
R
S
V
P
2.4.1
2.4.2
2.4.3
2.4.4
2.4.5
2.4.6
2.4.7
Construct an angle of 57°. Name the vertex V.
Extend the arms of the angle to make a pair of vertically opposite angles.
From V mark off VP and VR = 3,5 cm and VQ and VS = 5,5 cm
Join PQRS.
Check the sides and angles to see that you have a parallelogram.
Investiagte the diagonals you have drawn
Write the new facts you have learnt about a parallelogram on your table.
2.5
KITE
E
D
H
F
G
2.5.1
2.5.2
2.5.3
2.5.4
2.5.6
2.5.7
2.5.8
2.5.9
Draw a line segment DF 7 cm.
Draw the perpendicular bisector of DF.
Name the point where the lines cross H
On the bisector, mark off HE = 2 cm and HG = 5 cm.
Join DEFG.
Measure all the interior angles in this kite.
What else can you find out about the diagonals of the kite?
Write all the new facts about the kite on your table.
3.
Check your work! [5 mins]
If your work is neat and accurate you will have found the basic properties of quadrilaterals.
© e-classroom 2015
www.e-classroom.co.za
GR 9 3-5-7-2 LEARNERS
Page 4 of 4
4.
Going further!
4.1
4.2
4.3
Use the facts about angles to construct the different quadrilaterals you have drawn.
Make a quadrilateral family tree.
Make a collection of pictures of quadrilaterals used in architecture and manufacturing.
You could do a collection of pictures from old magazines and pamphlets or you could
make a digital collection on your device.
Which are the most common shapes?
Why do you think so?
Which are used the least often?
Why do you think this is so?
4.3.1
4.3.2
4.3.3
4.4.4
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