3. Given that the pairs of triangles shown are similar, fi nd the value of x. S
(i) S 11x – 4 70 70 T T 11x – 4 R R 60 60 D D 50 50 C C B B 5x + 11 U U
4. Consider the diagram shown. (i) Use Pythagoras’s theorem to fi nd the value of a . (ii) Show that the triangles ABE and ACD are similar. (iii) Use similar triangles to fi nd the value of x . (iv) Find the value of b .
5. Mark is 1·75 m tall and his shadow measures 7 m. A mobile phone mast casts a shadow of 56 m. Calculate the height of the mobile phone mast.
1.75 m 7 m 56 m
6. The diagram shown represents a player throwing a bounce pass, in which the angles formed by the basketball’s path are the same, to his teammate.
(i) Are the two triangles shown similar? Give reasons for your answer.
(ii) Calculate the height of the ball when it is caught by the teammate.
7. The penalty spot on a Gaelic football pitch is located on the perpendicular bisector of the goal line.
The width of the goal line is 6·5 m and the penalty spot is 11 m from the goal line.
(i) Using a scale of 1 : 100, construct a line segment to represent the goal line.
(ii) Construct the perpendicular bisector of your line segment and use it to show the position of the penalty spot.
84 cm (ii) V 5x + 11 V 88 88 W W S S24 24T 18 18 U U D b E a A 12 5 B 12 C x T