1. In. Prove the figure, AD//BC,AE//AD??? and p+q = 180. Prove that AB is // to EC
Angle p = angle ADE (base angles, isosceles triangle)
angle ADE = angle BCD (corresponding angles, AD//BC)
therefore, angle p =angle BCD
since, p+q=180 (given)
therfore, AB is // to EC (interior angle supplementary)
2. (a) let PR be x and PQ be 3x
x^2+9x^2 = 36^2 (Pythagorus theorem)
10x^2 = 1296
..................
PR= x = 11.384 (cor. to 3 d.p.)
PQ = 3x = 34.153 (cor. to 3 d.p.)
2(b) Area of PQR
(11.384x34.153)/2
= 194.4 cm square (cor. to 1 d.p.)