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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 c... 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
- Begin by drawing line segments AB and BC to form angle ABC.
- Using a compass, place the pointer on vertex B and draw an arc that intersects both sides of the angle (AB and BC) at points P and Q.
- Keeping the same radius, draw arcs centered at points P and Q, ensuring they intersect at point R.
- Draw a straight line from B through R. This line is the bisector of angle ABC.
Step 2
Construct the perpendicular bisector of BC.
Answer
- Identify points B and C on the line segment BC.
- Using a compass, measure the distance between B and C and halve it.
- With the compass set to this halfway distance, place the pointer on point B and draw an arc above and below the line BC.
- Repeat this step with the pointer placed on point C, creating two intersection points above and below the line.
- Draw a straight line through the intersection points; this line is the perpendicular bisector of BC.
Step 3
Shade the region which is - nearer to BC than to AB and - nearer to B than to C.
Answer
- To find the region nearer to line BC than line AB, locate the angle bisector created in part (a) and draw a perpendicular line to BC at an appropriate location.
- The area between this new line and line AB represents the region nearer to BC than AB.
- Next, to highlight the area closer to point B than point C, draw a perpendicular bisector to the line segment BC.
- The region that falls on the side of this bisector closer to point B should be shaded to illustrate that it is nearer to B than to C.
- The final shaded area is where these two conditions intersect.