1. Geometry CH 1-6 Basic Constructions End of Lecture / Start of Lecture mark

2. Geometry CH 1-6 Basic Constructions Objectives Students are able to identify the locus of a set of points that are: –at a given distance d from a given point O –at a given distance d from a given straight line –equidistant from two given points –equidistant from two given intersecting straight lines –locus of a set of points that satisfy the above conditions using a compass, ruler and protractor –a triangle given any three sides/angles using a ruler, compass and protractor

3. Geometry CH 1-6 Basic Constructions Objectives Students are able measure and construct key angles.  30 o Angle  45 o Angle  60 o Angle  90 o Angle

4. Geometry CH 1-6 Basic Constructions Measuring distance or Find the width of the picture.

5. Geometry CH 1-6 Basic Constructions Measuring Angles

6. Geometry CH 1-6 Basic Constructions At a given distance, d, from a given point A X d The locus is a circle with center A, and radius d cm.

7. Geometry CH 1-6 Basic Constructions The locus of points at a specific distance from a point.

8. Geometry CH 1-6 Basic Constructions Equidistant from two given points ABAB ( ( ( ( The locus is a perpendicular bisector of the line AB

9. Geometry CH 1-6 Basic Constructions Perpendicular Bisector

10. Geometry CH 1-6 Basic Constructions Perpendicular to a Line From a Point

11. Geometry CH 1-6 Basic Constructions Equidistant from two given intersecting lines ( ( ( The locus is the angle bisector of the angle between the two intersecting lines

12. Geometry CH 1-6 Basic Constructions Angle Bisector

13. Geometry CH 1-6 Basic Constructions Construct a 90 o angle

14. Geometry CH 1-6 Basic Constructions Construct a 60 o Angle

15. Geometry CH 1-6 Basic Constructions Construct a 45 o Angle

16. Geometry CH 1-6 Basic Constructions Construct a 30 o Angle

17. Geometry CH 1-6 Basic Constructions At a given distance, d, from a given straight line ABAB The locus is a pair of lines parallel to the given line, AB at a distance d cm from AB d d

18. Geometry CH 1-6 Basic Constructions Parallel Lines (Alternate Interior Angles Method)

19. Geometry CH 1-6 Basic Constructions Parallel Lines (Rhombus Method)

20. Geometry CH 1-6 Basic Constructions To be at right angle to a given line, AB A B The locus is a circle with center AB as the diameter of the circle

21. Geometry CH 1-6 Basic Constructions Example 1 Describe the locus of a point P, which moves in a plane so that it is always 4cm from a fixed point O in the plane. O X 4 cm The locus is a circle with center O, and radius 4cm.

22. Geometry CH 1-6 Basic Constructions Example 2 Describe the locus of a point Q, which moves in a plane, so that it is always 5 cm from a given straight line, l. l The locus is a pair of lines parallel to the given line, l, at a distance 5 cm from it. 5 cm

23. Geometry CH 1-6 Basic Constructions Example 3 Two points A and B are 7.5cm apart. Draw the locus of a point P, equidistant from A and B. A 7.5cmB ( ( ( ( The locus is a perpendicular bisector of the line AB

24. Geometry CH 1-6 Basic Constructions Example 4 Draw two intersecting lines l and m. Draw the locus of a point P which moves such that it is equidistance from l and m. ( ( ( The locus is the angle bisector of the angle between the two intersecting lines l m

25. Geometry CH 1-6 Basic Constructions Example 5 Construct an angle XYZ equal to 60 . Draw the locus of a point P, which moves such that it is equidistant from XY and YZ. ( ( ( The locus is the angle bisector of the angle between the two intersecting lines Z ( 60  Y X

26. Geometry CH 1-6 Basic Constructions Example 6 Construct the triangle ABC such that AB = 6cm, BC = 7cm and CA = 8cm. Draw the locus of P such that P is equidistant from A and C. A 6cmB C 8cm 7cm ( ( ( ( Locus of P

27. Geometry CH 1-6 Basic Constructions Example 7 Construct a triangle PQR in which QR = 8cm, angle RQP = 70  and segment RP = 9cm. Construct the locus which represents the points equidistant from PQ and QR. R 8cm Q P 9cm ( ( ( Locus ( 70 

28. Geometry CH 1-6 Basic Constructions Example 8 Constructing 60  angle Step 1: Construct Arc 1 Step 2: Construct Arc 2 Step 3:Draw line from intersectio n of two arc

29. Geometry CH 1-6 Basic Constructions Example 9 Construction of circumcircle ( ( ( ( ( ( ( ( Step 1:Draw perpendicular bisector of 1 side of triangle Step 2:Draw perpendicular bisector of 2nd side of triangle Step 3: Intersection of bisector will be the center of circle

30. Geometry CH 1-6 Basic Constructions Example 10: Construction of Inscribed Circle ( ( ( ( ( ( Step 1:Draw angle bisector on 1 st angle of triangle Step 2:Draw angle bisector of 2nd angle of triangle Step 3: Intersection of angle bisector will be the center of circle

31. Geometry CH 1-6 Basic Constructions Independent Practice-1 A long stick leans vertically against a wall. The stick then slides in such a way that its upper end describes a vertical straight line down the wall, while the lower end crosses the floor in a straight line at right angles to the wall. Construct a number of positions of the mid point of the stick and draw the locus.

32. Geometry CH 1-6 Basic Constructions

33. Geometry CH 1-6 Basic Constructions Intersection of Loci If two or more loci intersect at a point P, then P satisfies the conditions of the both loci simultaneously. Example: ABAB ( ( ( ( 6cm The circle is 6cm from point A. The perpendicular bisector is at equidistant from point A and B. XYXY The point X and Y are both at : i) 6 cm from A ii) Equidistant from point A and B

34. Geometry CH 1-6 Basic Constructions Do it Yourself! Question 1 a)Construct and label triangle XYZ in which XY=10cm, YZ=7.5cm and angle XYZ = 60 . Measure and write down the length of XZ. b)On your diagram, construct the locus of a point (i) 6cm from point Y (ii)equidistant from X and Z. c)The point P, inside the triangle XYZ is 6cm from Y and equidistant from point X and Y. (i)Label clearly, on your diagram, point P. (ii)Measure and write down the length of PX.

35. Geometry CH 1-6 Basic Constructions X Y Z

36. Geometry CH 1-6 Basic Constructions Do it Yourself! Question 5 A factory occupies a quadrilateral site ABCD in which AB=110m,  BAD=65 , AD=90m,  ADC=110  and DC=60m. (a) Using a scale of 1cm to represent 10m, construct a plan of the quadrilateral ABCD. Measure  ABC.

37. Geometry CH 1-6 Basic Constructions Two fuel storage tanks, T1 and T2 are located 30m from C and 15m from BD respectively. (b)On the same diagram, draw the locus which represents all the points inside the quadrilateral which are i) 30m from Cii) 15m from D (c)Mark clearly on your diagram, the positions of the tanks T1 and T2. (d)By measurement, find the distance between T1 and T2. Do it Yourself! (Continue)