Plane Geometry
22 Grade 8 Pre-Technical Studies questions on Plane Geometry, with worked marking schemes. 22 questions are available on this topic in full.
Question 1
3 marksA triangle has two angles measuring 50 degrees and 65 degrees.
(a) Calculate the third angle.
(b) State the type of triangle formed by these angles.
(3 marks)
Marking scheme
(a) 2 marks: 180 - (50 + 65) = 180 - 115 = 65 degrees (1 mark method, 1 mark answer). (b) 1 mark: Isosceles triangle (two angles equal - 65 and 65).
Question 2
1 markWhen bisecting a straight line of 8 cm using a pair of compasses, the compass radius should be set to:
A. Less than 4 cm
B. Exactly 8 cm
C. Exactly 4 cm
D. More than half the line length
(1 mark)
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1 markThe sum of the interior angles of any triangle is:
A. 180 degrees
B. 270 degrees
C. 90 degrees
D. 360 degrees
(1 mark)
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1 markIn a technical drawing, a triangle has all three sides measuring 5 cm. What is the correct name for this triangle?
A. Right-angled triangle
B. Scalene triangle
C. Isosceles triangle
D. Equilateral triangle
(1 mark)
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3 marksState three safety or accuracy precautions a learner should observe when doing geometrical construction in the workshop or classroom.
(3 marks)
Marking scheme
1 mark each (any 3): Keep the pencil sharp for thin accurate lines; handle the pointed compass carefully to avoid injury; use a clean drawing surface; hold instruments firmly to avoid slipping; do not press too hard so paper does not tear; store the compass point safely.
Question 6
1 markA learner is asked to construct an angle of 60 degrees using only a ruler and a pair of compasses, without a protractor. Which construction step produces exactly 60 degrees?
A. Drawing two perpendicular lines that cross
B. Bisecting a right angle to get two equal parts
C. Marking off an arc of the same radius from a point on a line and joining the intersection
D. Measuring one third of a straight angle with the ruler
(1 mark)
Marking scheme
C. Marking off an arc of the same radius from a point on a line and joining the intersection
Question 7
1 markA carpenter needs to check whether a corner joint of a table forms a perfect square corner. Which angle should the corner measure?
A. 60 degrees
B. 180 degrees
C. 45 degrees
D. 90 degrees
(1 mark)
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4 marksA learner is asked to construct an angle of 90 degrees at point P on a straight line using only a ruler and a pair of compasses. Describe the construction steps.
(4 marks)
Marking scheme
1 mark: With compass point at P, mark two equal arcs on the line, one on each side of P. 1 mark: From each of these two points, using a radius larger than the distance to P, draw arcs that intersect above the line. 1 mark: Join P to the point of intersection of the arcs. 1 mark: The line PQ is perpendicular to the original line, forming a 90-degree angle.
Question 9
4 marks(a) Name any two drawing instruments used in plane geometry construction.
(b) State one function of each instrument named.
(4 marks)
Marking scheme
(a) 2 marks (1 each): Any two of - pair of compasses, ruler, protractor, set square, T-square, pencil, divider. (b) 2 marks (1 each): Correct matching function, e.g. pair of compasses - draws circles/arcs; ruler - draws and measures straight lines; protractor - measures/draws angles; set square - draws parallel/perpendicular lines and standard angles.
Question 10
1 markTo divide a given angle into two equal parts, the correct construction is to:
A. Draw a perpendicular bisector
B. Inscribe a circle
C. Draw the angle bisector
D. Draw a tangent
(1 mark)
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4 marksExplain the difference between bisecting a line and bisecting an angle in plane geometry construction.
(4 marks)
Marking scheme
2 marks: Bisecting a line means dividing a straight line into two equal parts, usually with a perpendicular bisector through the midpoint. 2 marks: Bisecting an angle means dividing an angle into two equal smaller angles by drawing a line from the vertex through arcs of equal radius.
Question 12
1 markA quadrilateral has two pairs of parallel sides and all angles equal to 90 degrees, but adjacent sides are of different lengths. This shape is a:
A. Rhombus
B. Rectangle
C. Square
D. Trapezium
(1 mark)
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1 markA learner is asked in a drawing lesson to describe an angle that is greater than 90 degrees but less than 180 degrees. Which name should the learner give this angle?
A. Reflex angle
B. Acute angle
C. Right angle
D. Obtuse angle
(1 mark)
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1 markWhile constructing a regular hexagon for a workshop layout, a learner needs to recall how many equal sides this shape has. How many sides does a regular hexagon have?
A. Five
B. Seven
C. Six
D. Eight
(1 mark)
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1 markWhich instrument is most suitable for drawing accurate circles and arcs in plane geometry work?
A. Set square
B. T-square
C. Pair of compasses
D. Protractor
(1 mark)
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1 markAn angle measuring more than 90 degrees but less than 180 degrees is classified as:
A. Acute angle
B. Right angle
C. Obtuse angle
D. Reflex angle
(1 mark)
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1 markWhich pair of set squares is standard in a geometry drawing kit?
A. 45/60 degrees and 30/90 degrees
B. 90/90 degrees and 45/45 degrees
C. 30/30 degrees and 60/60 degrees
D. 30/60 degrees and 45/45 degrees
(1 mark)
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1 markTo construct a perpendicular bisector of a line, the two arcs must be drawn from:
A. One end of the line only
B. The centre of a circle
C. The midpoint of the line only
D. Both ends of the line
(1 mark)
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1 markA learner is asked in the workshop to construct an angle that measures exactly 90 degrees using only a pair of compasses and a ruler. What name is given to such an angle?
A. Right angle
B. Reflex angle
C. Acute angle
D. Obtuse angle
(1 mark)
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1 markA reflex angle is an angle whose size is:
A. Greater than 180 degrees but less than 360 degrees
B. Exactly 90 degrees
C. Between 90 and 180 degrees
D. Exactly 180 degrees
(1 mark)
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1 markA learner in a technical drawing lesson is asked to divide a given straight line into two equal parts and at the same time form a right angle to it. The line that does this is called the:
A. Diagonal
B. Arc
C. Perpendicular bisector
D. Tangent
(1 mark)
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1 markA learner draws a hexagon inside a circle where all six vertices touch the circle. This construction is called:
A. Tangent construction
B. Inscribing a hexagon
C. Circumscribing a hexagon
D. Bisecting a hexagon
(1 mark)
Marking scheme for this question
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