Practice questions 8.1


1. Draw a line segment of any length in your copybook. Mark any point p on the line segment. Draw a line perpendicular to your line segment through the point p , using a compass and straight edge.


2. (i)


Construct a line segment [AB] , 8 cm in length.


(ii) Construct the perpendicular bisector of [AB] . Mark the point of intersection of the bisector and [AB] , M .


(iii) Confi rm the perpendicular divides the


line segment [AB] in half by measuring |AM| and |BM| .


3. (i) Construct ∠XYZ of measure 60°. (ii) Construct the angle bisector of ∠XYZ .


(iii) Confi rm by measurement that ∠XYZ has been bisected.


4. Copy each of the following diagrams and construct a line perpendicular to the given line, through the given point. (i)


(ii) (iii) 7.


(i) Construct a triangle of sides 5 cm, 6 cm and 8 cm.


(ii) Measure the three angles inside the triangle and investigate if:


(a) the smallest angle is opposite the smallest side


(b) the largest angle is opposite the largest side.


8. (i) Construct a triangle DEF such that |DE| = 4 cm, |DF| = 6 cm and |∠EDF| = 40°.


(ii) Construct the perpendicular bisectors of each of the line segments [DE] , [DF] and [EF] .


(iii) The bisectors drawn in (ii) should intersect each other at a point. With this point of intersection as the centre, use a compass to draw a circle through D ,E and F . This circle is called the circumcircle.


9. (i) Construct a triangle TUV where |TU| = 6 cm, |∠VTU|= 50° and |∠VUT|= 2 |∠VTU| .


(ii) Construct the bisectors of each of the angles VTU, VUT, UVT .


(iii) The bisectors drawn in (ii) should intersect each other at a point. With this point of intersection as the centre, use a compass to draw a circle that fi ts exactly inside the triangle TUV , which touches all three sides of the triangle. This circle is called the incircle.


5. (i) Construct a rectangle of sides 6 cm and 8 cm.


(ii) Verify by measuring that both diagonals are equal in length.


6. (i) Construct an equilateral triangle PQR of side length 5 cm.


(ii) Measure the angles inside ΔPQR and use these measurements to confi rm that ΔPQR is equilateral.


10. (i) Construct the triangle XYZ with |XY| = 4 cm, |∠XYZ| = 90° and |∠YXZ| = 37°.


(ii) Measure the length of the sides [XZ] and [YZ] and use the converse of Pythagoras’s theorem to confi rm that triangle XYZ is a right-angled triangle.


11. (i) John wants to make a triangle with sides of length 5 cm, 2 cm and 10 cm. David thinks that John won’t be able to make this triangle. Give a reason why David is correct.


(ii) Change one of the lengths so that John will be able to form a triangle.


146 Linking Thinking 2


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