### Construction (I)

Construction of Lines and Angles

(1) Equidistant from a Point
Let the point be centre of the circle. The path that is equidistant from the centre would be the circumference of a circle.

(2) Equidistant from two Points
The perpendicular bisector to the line connecting the 2 points.

Point(s) to ponder:
• When marking the arcs from points A and B, why must we stretch the arm of the compass beyond half the length of AB?
• Why, to construct a perpendicular bisector, we have to keep the distance of the 2 arms of the compass the same? (i.e. we are actually drawing 2 circles of the same radius at points A and B respectively)
• What if the radii of the 2 circles (with centres at point A and point B) are different?

View clip to see how to construct the perpendicular bisector

(3) Equidistant from a line
Lines that are parallel to the given line; and these lines could be on either side of the given line.
Construct with a ruler and a set-square.

(4) Equidistant from a pair of non-parallel lines
When given 2 non-parallel lines, these lines will meet at some point. The angle bisector will lie between the two lines.

Point(s) to Ponder:
• What is the purpose of the first pair of arcs?
• For the second set of arcs, why only one pair is needed?
• Compare this to construction of a perpendicular bisector - which requires 2 pairs of intersecting arc.

View clip to see how to construct the angle bisector

(5) Construction of Triangles (Given 3 sides)
• What we need: A ruler (to draw the base of the triangle) & compass (to mark out the remaining sides of the triangle)
• Strategy - Planning: Sketch the diagram and put down all the information given in the question.

View clip to see how to construct a Triangle (given 3 sides)

(6) Construction of Triangles (Given 1 side and 2 angles)
• What we need: A ruler (for the base of the triangle) & protractor (for angle measurement)
• Strategy - Planning: Sketch the diagram and put down all the information given in the question.

View clip to see how to construct a Triangle (given 1 side & 2 angles)

(7a) Construction of Triangles (Given 2 sides and 1 angle)
• What we need: A ruler (for the base of triangle), a compass (for the remaining side of the triangle) and a protractor (for the angle)
• Strategy - Planning: Sketch the diagram and put down all the information given in the question.

View clip to see how to construct a Triangle (given 2 sides & 1 angle)

(7b) Construction of Triangles (Given 2 sides and 1 angle)
• What we need: A ruler (for the base of triangle), a compass (for the remaining side of the triangle) and a protractor (for the angle)
• Strategy - Planning: Sketch the diagram and put down all the information given in the question.

View clip to see how to construct a Triangle (given 2 sides & 1 angle)

(8) Construction of Triangles (Given 3 angles)

• What we need: A ruler (for the base of triangle) and a protractor (for the angles)
• Strategy - Planning: Sketch the diagram and put down all the information given in the question.

Point(s) to ponder:

• Is there any redundant information given in the question?

View clip to see how to construct the Triangle, given 3 angles