**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*

Thank You for going through those questions!

ReplyDeleteYou are most welcome :)

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