Bisect Angle Triangle Given Sides and Angle Circumcircle Incircle Triangle Given Three Sides Bisect Line Centroid

Bisect the given angle BAC without using a protractor. Show all construction lines. B C  A

Construct the perpendicular bisector of line segment [AB]. Show all construction lines. B  A

Construct a triangle ABC with | AB | = 6 cm, |  BAC | = 50º and |  ABC | = 70º. Label your diagram clearly. C 50º 70º  6 cm A B

LCO 2008 Paper 2 Question 4 (c) (i) Construct an equilateral triangle PQR of side 8 cm. 60º Angles in an equilateral triangle are all 60º Q P R

Set your compass so that the pencil and point are 2·5 cm apart With B as centre draw an arc with the point of the compass Similarly draw an arc with your compass set at 6 cm and with A as the centre Draw the base line AB 6·5 cm in length 6·5 cm C B Mark the intersection of the arcs as C and draw the lines AC and BC (i) Construct a triangle ABC in which | AB | = 6·5 cm, | BC | = 2·5 cm and | AC | = 6 cm. A 10 6 cm 2·5 cm LCO 2006 Paper 2 Question 4 (c) (i)

P Q R Construct a triangle PQR with | PQ | = 8 cm, | QR | = 10 cm and |  PQR| = 30º. Label your diagram clearly. 30º  10 cm 8 cm

Y With X as centre draw an arc Show how to construct the triangle XYZ, with sides | XY | = 10 cm, | XZ | = 8 cm and | YZ | = 5 cm. Mark the intersection of the arcs as Z and draw the lines XZ and YZ Set your compass so that the pencil and point are 8 cm apart Similarly draw an arc with your compass set at 5 cm and with Y as the centre Draw the base line [XY] 10 cm in length X Z 10 5 cm 10 cm 8 cm  JCH 2010 Paper 2 Question 3 (b) (i)

Mark the intersection of the arcs and draw the lines With the end point as centre draw an arc Set your compass so that the pencil and point are 6 cm apart Similarly draw an arc with your compass set at 8 cm and with the start point as the centre Construct a triangle of sides 11 cm, 8 cm and 6 cm. JCH 2008 Paper 2 Question 3 (b) (i) Draw the base line 11 cm in length 20  6 cm 11 cm 8 cm

Draw the base line 8 cm in length Set your compass so that the pencil and point are 6 cm apart Similarly draw an arc with your compass set at 7 cm and with the start point as the centre Mark the intersection of the arcs and draw the lines Construct a triangle of sides 8 cm, 7 cm and 6 cm. All construction lines must be clearly shown in each case. With the end point as centre draw an arc 10  JCH 2006 Paper 2 Question 3 (c) (i) 6 cm 8 cm 7 cm

Similarly draw an arc with your compass set at 7 cm and with Y as the centre Draw the base line [XY] 10 cm in length Construct a triangle XYZ in which | XY | = 10 cm, | YZ | = 7 cm and | XZ | = 5 cm. Mark the intersection of the arcs as Z and draw the lines XZ and YZ Set your compass so that the pencil and point are 5 cm apart With X as centre draw an arc Y X Z 10 JCH 2003 Paper 2 Question 3 (b) (i) 7 cm 10 cm 5 cm

Construct the incircle of the triangle. All construction lines must be clearly shown in each case.  Construct the bisector of two of the angles using circle arcs The intersection of the bisectors is the centre of the incircle 10 JCH 2006 Paper 2 Question 3 (c) (ii)

JCH 2009 and 2004 Paper 2 Question 4 (b) Show how to construct the circumcircle of a triangle. All construction lines must be clearly shown.  B A C Construct the perpendicular bisector of [AB] using circle arcs. Construct the perpendicular bisector of [AC] using circle arcs. The bisectors meet at O the circumcentre of the triangle. O Using O as centre and |OC| as radius construct the circumcircle.

B A C LCO 2011 Project Maths Paper 2 Question 6A (a) Show how to construct the centroid of a triangle. All construction lines must be clearly shown. Construct the perpendicular bisector of [AB] using circle arcs. Construct the perpendicular bisector of [AC] using circle arcs. The medians meet at O ,the centroid of the triangle. Join the perpendicular of [AB] to vertex C. Join the perpendicular of [AC] to vertex B. O 15

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