In the figure A and B are points on PQ and PR
such that AB || QR.
AR and BQ are drawn.
Answer the following questions, which refer to
a theorem. You need to redraw the sketch.
1.1 Complete: ΔΔ area/APB area AQB = . . . . . . . .
1.2 Complete: ΔΔ area/APB area ABR = . . . . . . . .
1.3 What can you say about the area of ΔAQB and the area of ΔABR, and why?
1.4 What can you deduce from 1.1, 1.2 and 1.3?
1.5 Give the wording of the theorem which is under consideration here.
1.1 Complete: ΔΔ area/APB area AQB = BQ^2/PQ^2
1.2 Complete: ΔΔ area/APB area ABR = AR^2/PR^2
1.3 The area of ΔAQB is proportional to the area of ΔABR, because they share the same base AB and have equal heights.
1.4 From 1.1, 1.2, and 1.3, we can deduce that the ratio of the areas of similar triangles is equal to the square of the corresponding sides.
1.5 The theorem under consideration here is the Triangle Area Proportionality Theorem.