How to Solve Mathematics Construction Questions, Practical Tips for Beginners
If you have a problem dealing with construction then this content is for you. In this content, we shall provide with over 10 different construction strategies and how to go about them.
We shall be focusing on constructing general shapes and constructing particular angles.
Note both the BECE and WASSCE exams, candidates are examined on constructions. For this reason, you need to master them at all cost.
Have some seat, your mathematical sets, popcorn, fruit juice as we delve into these construction tips;
How to Solve Mathematics Construction Questions, Practical Tips for Beginners
(1) Construct a perpendicular bisector to a line segment AB. Steps:
Draw line segment AB with endpoints A and B.
With A as the center and a radius greater than half of AB, draw an arc that intersects AB at two points.
Repeat with B as the center and the same radius to draw another arc that intersects AB at two points.
Draw a straight line through the two points of intersection, which will be perpendicular to AB and will bisect it.
(2) Construct a triangle ABC with sides AB = 4 cm, BC = 6 cm, and AC = 5 cm. Steps:
Draw line segment AB with length 4 cm.
At point A, draw an arc with radius 5 cm.
At point B, draw an arc with radius 6 cm.
The intersection of these arcs will be point C.
Connect points A, B, and C to form triangle ABC.
(3) Construct an equilateral triangle with side length 3 cm. Steps:
Draw a line segment of length 3 cm.
At one endpoint of the segment, draw an arc with radius 3 cm.
Repeat at the other endpoint of the segment.
Connect the endpoints of the arcs to form an equilateral triangle.
(4) Construct an angle of 60 degrees. Steps:
Draw a line segment AB.
Place the compass point at A and draw an arc that intersects AB.
Without changing the compass width, place the compass point at the intersection and draw another arc.
Repeat the process from B to get a second intersection.
Draw a straight line from A through the second intersection to create a 60 degree angle.
(5) Construct a square ABCD with side length 5 cm. Steps:
Draw a line segment AB of length 5 cm.
At B, draw an arc with radius 5 cm.
At D, draw an arc with radius 5 cm.
Connect the endpoints of the arcs to create a line segment.
Repeat the process from A and C to get the other two sides of the square.
(6) Construct a rhombus ABCD with side length 6 cm and angle BAD = 60 degrees. Steps:
Draw a line segment AB of length 6 cm.
Draw a line through A that makes a 60 degree angle with AB.
At the intersection of the line and AB, draw a line perpendicular to AB.
The intersection of the perpendicular line with the line through A is point C.
Repeat the process from B to get point D.
Connect points A, B, C, and D to form a rhombus.
(7) Construct a regular hexagon with a side length of 4 cm. Steps:
Draw a line segment of length 4 cm.
At one endpoint, draw an arc with radius 4 cm.
Repeat this process, using the endpoint of the arc as the center of the next arc, until you have six intersecting points.
Connect the intersecting points to form a regular hexagon.
(8) Construct a circle with center O and radius 3 cm. Steps:
Draw a point O to represent the center of the circle.
Place the compass point at O and draw an arc with radius 3 cm.
The arc represents the circle.
(9) Construct a line parallel to line AB that passes through point C. Steps:
Draw line segment AB and point
constructing angles
(10) Construct an angle of 30 degrees. Steps:
Draw a line segment AB.
Place the compass point at A and draw an arc that intersects AB.
Without changing the compass width, place the compass point at the intersection and draw another arc.
The distance between the two intersections should be less than the length of AB.
Draw a straight line from A to the second intersection to create a 30 degree angle.
(11) Construct an angle of 45 degrees. Steps:
Draw a line segment AB.
Place the compass point at A and draw an arc that intersects AB.
Without changing the compass width, place the compass point at the intersection and draw another arc.
The distance between the two intersections should be the same as the length of AB.
Draw a straight line from A through the second intersection to create a 45 degree angle.
(12) Construct an angle of 120 degrees. Steps:
Draw a line segment AB.
Place the compass point at A and draw an arc that intersects AB.
Without changing the compass width, place the compass point at the intersection and draw another arc.
The distance between the two intersections should be greater than the length of AB.
Draw a straight line from A to the second intersection to create a 120 degree angle.
(13) Construct a line perpendicular to AB that passes through point C. Steps:
Draw line segment AB and point C.
With C as the center and a radius greater than half of AB, draw an arc that intersects AB at two points.
Draw two arcs of the same radius with the two points of intersection as centers.
The intersection of the two arcs will be the midpoint of AB.
Draw a straight line through the midpoint of AB and point C to create a line perpendicular to AB that passes through point C.
(14) Construct a line that is parallel to line AB and passes through point C. Steps:
Draw line segment AB and point C.
Place the compass point at C and draw an arc that intersects AB.
Without changing the compass width, place the compass point at the intersection and draw another arc.
Draw a straight line through point C and the second intersection. This line will be parallel to AB and will pass through point C.
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