7. Two boats started at the same point. After 2 hours, one boat had travelled 28 km due east. The other boat had travelled 45 km due north. How far apart are the boats at this time?
N 16 cm 56 cm D E C
8. (i) Find |BD| (ii) Hence, fi nd |CD|
A 63 cm B
22B Taking it FURTHER
1. The triangle PQR is an isosceles triangle. PS is perpendicular to QR .
Use congruent triangles to show that |SQ| = |SR| .
P
3. ABCD is a kite. |AB| = |AD| and |BC| = |CD|
(i) Show that triangles ABC and ADC are congruent.
B A Q
2. PQRS is a rectangle. P
M T S U S R E D Q N R
M is the midpoint of [PQ] , N is the midpoint of [QR] .
T is the midpoint of [PS] and U is the midpoint of [RS] .
(i) Show that the triangles PMT and RUN are congruent.
(ii) Are the line segments [TM] and [UN] equal? Justify your answer.
(iii) Is the triangle STU congruent to the triangle RNU ? Justify your answer.
12 m
(ii) The line joining B to D meets the diagonal AC at E and BD is perpendicular to AC. Explain why triangles ABE and ADE are congruent.
4. A town council wants to put a skateboard ramp into a local park.
(i)
If the ramp has the dimensions shown below, calculate the length, to the nearest metre, of the ramp along the ground.
(ii) If Becky travels at an average speed of 4 m/s, how long will it take her to travel from the top to the bottom of the ramp?