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ABCD is a quadrilateral - OCR - GCSE Maths - Question 5 - 2020 - Paper 1
Question 5
ABCD is a quadrilateral. a) Construct the bisector of angle ABC. Show all your construction lines. b) Construct the perpendicular bisector of BC. Show all your con... show full transcript
Worked Solution & Example Answer:ABCD is a quadrilateral - OCR - GCSE Maths - Question 5 - 2020 - Paper 1
Step 1
Construct the bisector of angle ABC.
Answer
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Place the compass point at point B and draw an arc that intersects both lines AB and BC. Let these points of intersection be E and F respectively.
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Without changing the compass width, place the compass point on point E and draw an arc inside angle ABC.
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Then, place the compass point on point F and draw another arc that intersects the previous arc. Let the intersection point be G.
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Draw a straight line from B to G; this line is the bisector of angle ABC.
Step 2
Construct the perpendicular bisector of BC.
Answer
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Place the compass point at point B and set the compass to a width greater than half the length of BC. Draw arcs above and below line BC to create intersection points.
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Repeat the same step with the compass point at point C, ensuring the width is unchanged, to create new intersection points.
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Draw a straight line through the intersection points; this line is the perpendicular bisector of BC.
Step 3
Shade the region which is nearest to BC than to AB and nearer to B than to C.
Answer
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Identify the region bounded by the angle bisector of angle ABC and the perpendicular bisector of line segment BC.
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Shade the area that is closer to line BC than to line AB and closer to point B than point C. This shaded region will be inside the triangle formed by the lines AB, BC, and the bisectors constructed.