This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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4. Using a compass, go through the steps for constructing a line labelled CD perpendicular to both sides of a line labelled AB.
This describes constructing a perpendicular bisector of a line segment AB.
Step 1: Draw a line segment and label its endpoints A and B. Step 2: Place the compass point on A and open it to a radius greater than half the length of AB. Draw an arc above and below the line segment AB. Step 3: Without changing the compass radius, place the compass point on B and draw another arc above and below the line segment AB, intersecting the first two arcs. Step 4: Label the two points where the arcs intersect as C and D. Step 5: Use a ruler to draw a straight line segment connecting point C and point D. This line CD is perpendicular to AB and bisects AB.
5. Label the circle.
a) Use the following words: chord, diameter, radius and centre. On the provided circle diagram:
b) Draw a circle with a diameter of .
Step 1: Calculate the radius. The radius is half of the diameter. Step 2: Open your compass to a width of using a ruler. Step 3: Place the compass point on your paper and rotate the compass to draw a complete circle.
6. Draw an equilateral, isosceles and a scalene triangles. Label each triangle.
a) Equilateral triangle: An equilateral triangle has all three sides equal in length and all three angles equal to . To draw it: Draw a line segment for the base. Set your compass to the length of this base. From each endpoint of the base, draw an arc above the base. The point where the arcs intersect is the third vertex. Connect this point to the two base endpoints.
b) Isosceles triangle: An isosceles triangle has two sides equal in length and the two angles opposite these sides are equal. To draw it: Draw a base line segment. From the midpoint of the base, draw a perpendicular line upwards. Choose a point on this perpendicular line as the third vertex. Connect this vertex to the two endpoints of the base. Alternatively, draw a base, then set your compass to a desired length for the equal sides. From each endpoint of the base, draw an arc with this length. The intersection is the third vertex.
c) Scalene triangle: A scalene triangle has all three sides of different lengths and all three angles of different measures. To draw it: Draw a line segment for the base. Choose two different lengths for the other two sides. Set your compass to the first length and draw an arc from one endpoint of the base. Set your compass to the second length and draw an arc from the other endpoint of the base. The intersection of these arcs is the third vertex. Connect this vertex to the two base endpoints.
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4. Using a compass, go through the steps for constructing a line labelled CD perpendicular to both sides of a line labelled AB.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.