In the figure A and B are points on PQ and PR

Question

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: ΔareaAPB/Δarea AQB = . . . . . . . .
1.2 Complete: ΔareaAPB/Δarea 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.

Answer 1

1.1 Complete: ΔareaAPB/Δarea AQB = AQ/AP
1.2 Complete: ΔareaAPB/Δarea ABR = AR/BP
1.3 The area of ΔAQB is proportional to the area of ΔABR because their bases are parallel to each other.
1.4 From 1.1, 1.2, and 1.3, we can deduce that the ratio of the areas of two triangles with a common baseline is equal to the ratio of the lengths of the segments on that baseline.
1.5 The theorem under consideration here is the Intercept theorem.