Practice questions 3.2


1. State whether the following lines are parallel, perpendicular, or neither. Give a reason for each answer, and express the relationship between the lines in mathematical language, using symbols and numbers where possible.


(i) D C D B (iii) A D B C C (iv) D B 7.


2. (i) Draw a line segment [MN] of length 10 cm . Mark a point 5 cm anywhere directly above this line, and label it Q .


(ii) Construct a line parallel to MN which passes through Q .


(iii) How could you confi rm the line you have drawn is parallel to [MN] ?


3. (i)


Draw a line segment [XY] of length 120 mm using only a ruler. Mark a point 70 mm anywhere directly above this line, and label it W.


(ii) Construct a line parallel to [XY] which passes through W .


(iii) How could you confi rm the line you have drawn is parallel to [XY] ?


4. (i)


Draw a line segment [AB] of length 9 cm using only a ruler. Mark a point 4·5 cm from one end of this line, and label it Q .


(ii) Construct a line perpendicular to [AB] at point Q .


(iii) How could you confi rm the line you have drawn is perpendicular to [AB] ? (Hint: use a set square)


C A B A (ii) A 5. (i)


Draw a line segment [XY] of length 100 mm . Mark a point 5·5 cm from one end of this line, and label this point N .


(ii) Construct a line perpendicular to [XY] at point N .


(iii) How could you confi rm the line you have drawn is perpendicular to [XY] ?


6. (i)


Draw a line segment [PQ] of length 85 mm . Mark a point 4·7 cm anywhere directly above this line, and label it A.


(ii) Construct a line parallel to PQ which passes through A.


(iii) How could you confi rm the line you have drawn is parallel to [PQ] ?


(i) Draw a line segment [PQ] of length 9 cm .


(ii) Construct the perpendicular bisector of [PQ] and hence mark the midpoint of [PQ]


(iii) How could you check the line you have drawn is both a bisector of [PQ] and perpendicular to [PQ] ?


8. (i) Draw a line segment [MN] of length 10 cm .


(ii) Construct the perpendicular bisector of [MN] and hence mark the midpoint of [MN]


(iii) How could you check the line you have drawn is both a bisector of [MN] and perpendicular to [MN] ?


9. (i) Construct [AB] if |AB| = 11 cm.


(ii) Construct the perpendicular bisector of [AB] and hence mark the midpoint of [AB] .


(iii) How could your check the line you have drawn is both a bisector of [AB] and perpendicular to [AB] ?


10. The blue line in the circle below is the radius of the circle and the red line touches the circle once and only once. Are the lines perpendicular?


48


Linking Thinking 1


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