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The diagram shows triangle ABC - OCR - GCSE Maths - Question 7 - 2018 - Paper 4
Question 7
The diagram shows triangle ABC. (a) Construct the bisector of angle BAC. (b) Construct the perpendicular bisector of AC. (c) Shade the region inside triangle ABC th... show full transcript
Worked Solution & Example Answer:The diagram shows triangle ABC - OCR - GCSE Maths - Question 7 - 2018 - Paper 4
Step 1
Construct the bisector of angle BAC.
Answer
To construct the bisector of angle BAC, place the compass point on vertex A and draw an arc that crosses both sides of the angle, extending into the triangle. Label the intersection points as D and E. Then, without changing the compass width, place the compass point on D and draw an arc inside the angle. Repeat this process from point E, creating a second arc that intersects the first arc. Label the intersection of these arcs as F. Finally, draw a straight line from A through point F. This line is the angle bisector of BAC.
Step 2
Construct the perpendicular bisector of AC.
Answer
To construct the perpendicular bisector of segment AC, first measure the distance between points A and C. Without changing the compass width, place the compass point on A and draw an arc above and below AC. Then, without adjusting the compass, place the compass point on C and draw another pair of arcs that intersect the previous arcs. Label the intersections as G and H. Finally, draw a straight line connecting points G and H. This line is the perpendicular bisector of AC.
Step 3
Shade the region inside triangle ABC that is nearer to AC than to AB and nearer to A than to C.
Answer
To shade the correct region inside triangle ABC, first focus on the area nearer to AC than AB. Identify the angle's interior and shade the region closer to line AC. Then, determine the area closer to point A than to C, typically located towards A and away from C inside the triangle. The intersection of these two regions will define the final shaded area inside triangle ABC.