CONSTRUCTION Designed and compiled by Menu Construction 1
CONSTRUCTION Designed and compiled by
Menu Construction 1 a Construct a triangle (ASA) Construction 1 b Construct a triangle (SAS) Construction 2 Construct the bisector of an angle Construction 3 Construct the perpendicular bisector of a line segment. Construction 4 Construct the circumcircle of a triangle. Construction 5 Construct the incircle of a triangle. Construction 6 Divide the line segment [ab] into three equal parts.
Construct the triangle PQR where |QR|=8 cm, | PQR|=52 o and | PRQ|=46 o (A S A) • Draw a line segment [QR] 8 cm in length. Name the points and mark the length. • 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. P 52° Q END OF |QR|=8 c m CONSTRUCTION 46° Quit R Menu
Construct a triangle ABC where |AB| = 12 cm, | BAC|=65 o and |AC| = 9 cm (S A S) USE MOUSE CLICKS TO VIEW CONSTRUCTION • Draw a line segment 12 cm 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 9 cm radius to draw an arc on this line. • Mark the point of intersection C. C |AC |=9 cm • Join C to B and complete labels. 65° A Quit |AB|=12 cm END OF CONSTRUCTION b Menu
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. A X O X X Quit Y B END OF CONSTRUCTION Menu
Construct the perpendicular bisector of a line segment • • Draw the line segment 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. A B Quit END OF CONSTRUCTION Menu
Construct the circumcircle of a triangle A O C B • • Draw the triangle ABC 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 END OF CONSTRUCTION Quit Menu
Construct the incircle of a triangle A O X • • • B X 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 END OF CONSTRUCTION O O C Quit Menu
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| A C D B R S T END OF CONSTRUCTION Quit Menu
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