Thi» chapter is concerned with the construction of plane geometric figures. Plane geometry is the geometry of figures that are two-dimensional, i.e figures that have only length and breadth. Solid geometry is the geometry of three-dimensional figures.
F«g. 2/1 To construct a parallel line
Fig 2/2 To bisect a line
There are an endless number of plane figures but we will concern ourselves only with the more common ones —the triangle, the quadrileteral and the better known
Before we look at any particular figure, there are a few constructions that must be revised.
Fig. 2A To erect a perpendicular from a point to a line
Fig. 2A To erect a perpendicular from a point to a line
Fig 2/3 To erect a perpendicular from a point on a line Fig. To bisect the angle formed by two converging li
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THE TRIANGLE
Definitions
The triangle it a plane figure bounded by three straight sides.
A sceiene triangle is a triangle with three unequal sides and three unequal angles
An isoscefes triangle is a triangle with two sides, and hence two angles, equal.
An equUetere! triangle is a triangle with ell the sides, and hence all the angles, equal.
A right-angled triangle is e triangle containing one right angle. The aide opposite the right-angle is called the hypotenuse.
Constructions
To construct en equileters! triangle, given one of the sides (Fig. 2/14)
1. Draw a line AS. equal to the length of the aide.
3. With compess point on B, and with the same radius.
draw another arc to cut the first arc at C. Triangle ABC is equilateral.
To construct en Isósceles triangle given the perl-meter and the altitud« (F'ig. 2/15)
1. Draw line AB equsl to hatf the perimeter.
2. From Berecte perpendicular and meke BCequalto the etthude.
4. Produce DB so that BE — BD. C D E is the required triangle.
To construct a triangle, given the base angles end the altitude (Fig. 2/16)
2. Construct CD parallel to AB so that the distance between them is equal to the altitude.
3. From any point E. on CD, draw CEF and DEG so that I bey cut AB in F and G respectively.
Since C£F - EFG and DEG - EGF (alternate engles). then EFG is the required triangle.
To construct a triangle given the base, the altitude and the vertical angle ( Fig. 2/17)
1. Draw the base AB
2. Construct BÂC equal to the vertical angle
3. Erect AD perpendicular to AC.
5. With centre O and radius OA (- OB), draw a circle.
6. Construct EF parallel to AB so that the distance between them is equal to the altitude.
Let EF intersect the circle in G. ABG is the required triengle.
To construct a trlanola given the perimeter end the ratio of tht si des (Fig 2/18)
1. Draw the line AB equal in length to the penmeter.
2. Divide AB into the required ratio (say 4:3:8).
To construct a trlanola given the perimeter end the ratio of tht si des (Fig 2/18)
1. Draw the line AB equal in length to the penmeter.
2. Divide AB into the required ratio (say 4:3:8).
2. Produce 8C in both directions.
3. With compass point on B and radius BA. draw an arc to cutC8 produced in P.
4. With compass point on C and radius CA. draw an arc to cut BC produced in E.
5. Draw a line FG equal in length to the required perimeter.
8 Join EG and draw CJ and BH parallel to it
7. With centre H and radius H F draw an arc.
8. With centre J and radius JG draw another arc to intersect the first arc in K.
HKJ is the required triangle
THE QUADRILATERAL
Definition»
The quedrileteral is a plane figure bounded by four straight sides.
A iqutre is a quadrilateral with all four sides of equal length and one of its angles (and hence the other three) a right angle.
A rectangle is a quadrilateral with its opposite sides of equal length and one of its angles (and hence the other three) a right angle.
A parallelogram is a qusdnlateral with opposite sides equal and therefore parallel. A rhombus is a quadrilateral with all four sides equal. A trapezium is a quadrilateral with one pair of opposite sides parallel
A trapezoid is a quadnlateral with all four sides and angles unequal.
Constructions
To construct e square given the length of the aide (Fig. 2/21)
1. Drew the side AB.
2. From B erect a perpendicular.
3. Mark off the length of side BC.
4. With centres A and C draw arcs, radius equal to the length of the side of the square, to intersect at D.
ABCD is the required square.
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