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Construction 1a Construct a triangle (ASA) Construction 1a Construct a triangle (ASA) Construction 1b Construct a triangle (SAS) Construction 1b Construct a triangle (SAS) Construction 2 Construct the bisector of an angle Construction 2 Construct the bisector of an angle Construction 3 Construct the perpendicular bisector Construction 3 Construct the perpendicular bisector of a line segment. of a line segment. Construction 4 Construct the circumcircle of a triangle. Construction 4 Construct the circumcircle of a triangle. Construction 5 Construct the incircle of a triangle. Construction 5 Construct the incircle of a triangle. Construction 6 Divide the line segment [ab] into three Construction 6 Divide the line segment [ab] into three equal parts. equal parts.

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Construct the triangle PQR where |QR|=8cm, | PQR|=52 o and | PRQ|=46 o (A S A) Draw a line segment [QR] 8cm in length. Name the points and mark the length. |QR|=8c m 46° 52° P RQ At Q using a protractor mark and draw an angle of 52 o. At R mark and draw an angle of 46 o Mark the point of intersection of the two angles. This is the point P. Quit Menu END OF CONSTRUCTION

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Construct a triangle ABC where |AB| = 12cm, | BAC|=65 o and |AC| = 9 cm (S A S) 65° bA C |AB|=12cm |AC|=9cm Menu Quit USE MOUSE CLICKS TO VIEW CONSTRUCTION END OF CONSTRUCTION Draw a line segment 12cm in length. Name the points and mark the length. Use a protractor to draw a line at 65 o to |AB|. Use a compass with A as centre and 9cm radius to draw an arc on this line. Mark the point of intersection C. Join C to B and complete labels.

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Construct the bisector of an angle Draw the angle AOB. Using the vertex o as centre draw an arc to meet the arms of the angle at X and Y. Using X as centre and the same radius draw a new arc. Using Y as centre and the same radius draw an overlapping arc. Mark the point where the arcs meet. The bisector is the line from O to this point. Y X O A B X X Menu Quit END OF CONSTRUCTION

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Construct the perpendicular bisector of a line segment Draw the line segment AB Menu Quit END OF CONSTRUCTION Using A as centre and a radius greater than half |AB| draw an arc. Using B as centre and the same radius draw another arc. Draw a line through the points where the arcs cross.

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Construct the circumcircle of a triangle Draw the triangle ABC O A B C Menu Quit END OF CONSTRUCTION Construct the perpendicular bisector of [AB] Construct the perpendicular bisector of [AC] The bisectors meet at O the circumcentre of the triangle Using O as centre and |OA| as radius construct the circumcircle of the triangle ABC

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Construct the incircle of a triangle Menu Quit END OF CONSTRUCTION Draw the triangle ABC Construct the bisector of angle ABC as shown. Construct the bisector of angle ACB as shown. The bisectors meet at point O, the incentre of the triangle Using O as centre construct the incircle of the triangle ABC O O X X O A B C

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Divide the line segment [AB] into three equal parts Draw the line segment [AB]. Through A draw a line at an acute angle to [AB]. On this line use circle arcs of the same radius to mark off three segments of equal length [AR], [RS] and [ST]. Join T to B. Through S and R draw line segments parallel to [TB] to meet [AB] at D and C. Now |AC|=|CD|=|DB| DC T S AB R Menu Quit END OF CONSTRUCTION

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