 Triangle FGH where GH = 6,2 cm; \(\hat{G}\) = 36\(^\circ\) and \(\hat{H}\) = 63\(^\circ\)
 Parallelogram PQRS where PQ = 5,7 cm, PS = 7,8 cm and \(\hat{R}\) = 112\(^\circ\)
 Construct \(\triangle\)KLM where KL = 9,4 cm; LM = 7 cm and MK = 7,8 cm.
 Construct the perpendicular bisectors of all three sides of the triangle drawn in part (a). You should find that they all go through the same point.
 Use the point of intersection as the midpoint of a circle that passes through all three vertices of the triangle. Use your compass to draw this circle.
 45\(^\circ\)
 210\(^\circ\)
 Construct a horizontal line, AB, which is 2 cm long.
 Set your compass to 2 cm, and from each of A and B, draw an arc above line AB. Call the point that the arcs intersect O.
 Draw a circle of radius 2 cm, centred on O. It should go through A and B.
 Place the compass on point B, and draw an arc crossing the circle on the side opposite to A. Call this point C.
 Repeat the above step to create points D to F.
 Join B to C with a straight line. Repeat with C to D, and so on, until you get back to point A. You have now constructed a regular hexagon!
Parallelogram 
Rectangle 
Square 
Rhombus 
Trapezium 
Kite 

Diagonals bisect each other 

Diagonals cut at right angles 
Study the following figure. Note that \(d\), \(e\) and \(f\) are the exterior angles of the triangle.
 Write down an equation that shows the
relationship between angle d and the sum of two other
angles in the image.
 Determine the size of d + e + f. Give reasons for your
answer.
Note: the triangles are not drawn to scale.
Prove that \(\triangle\)SRP \(\) \(\triangle\)SQT.

 Given: EH = EJ

\(A\hat{B}G = x\); \(B\hat{C}D = 130^\circ\) and \(C\hat{D}J = 72^\circ\)

 BF = 8 cm; BC = 10 cm; FD = 6 cm
 GI = 12 cm; JK = 6 cm and JK : KH = 1 :
2
 The shape alongside is that of a
window, consisting of a rectangular section HJKL, and a
semicircular top section. HJ = 0,5 m and JK = 0,2 m.
 Area of the rectangle
 Perimeter of the rectangle
Rectangle 
Triangle 
Circle 

New perimeter/circumference 

New area 
\(2y\) 
 Construct a triangle RST with RS = 7,3 cm, \(\hat{R}\) = 42\(^\circ\); and \(\hat{S}\) = 67\(^\circ\). (
Use a protractor and ruler to check that the learners' constructions are accurate. Allow an error of up to 1 mm and 1\(^\circ\).
 Construct the bisectors of each of the angles of the triangle that you constructed in part (a). You should find that they have a common point of intersection.
 Use the common point of intersection of the bisectors of the angles that you constructed in part (b) as the midpoint of a circle touching all three sides of the triangle. Use your compass to draw this circle.
 Is it always possible to draw
a triangle given the length of one of the lines and the sizes
of the angles adjacent to that line (as was given in part (a),
for example)? Explain your answer.
 Construct the following angle
without using a protractor: 150\(^\circ\).
 Mthunzi is thinking of a
quadrilateral and provides the following clue to Sam: "Its
diagonals cut perpendicularly, but not all the sides of the
shape are equal in length." Help Sam by writing down the
special name of the shape.
 Look at the figure below.
Write down an equation, and use it to determine the size of
x. (3)
 Prove that \(\triangle\)JNM
\(\equiv\)
\(\triangle\)KNL.
 Do you have enough
information to prove that \(\triangle\)JLM \(\equiv\)
\(\triangle\)KML? Explain your answer.
 Study the diagram alongside:
Given that \(\triangle\)CDE \(\equiv\) \(\triangle\)FCG, prove that ED \(\) GF. Give reasons for all statements.
 Briefly explain why
\(\triangle\)ABF \(\) \(\triangle\)ACD (a full
proof is NOT required).
 Use the similarity of the
triangles to determine the lengths of the line segments
(correct to one decimal place).
 \(x\)
 \(y\)
 \(x\)
 Calculate the length of UT.
 Calculate the perimeter of
triangle TUV, correct to one decimal place.
 Calculate the length of a
side of the rhombus.
 Show that the area of the
rhombus is 216 cm^{2}.