Geometry

2.    Constructing a figure based on the given conditions

In this question, let x=4, and y=12 be your lucky numbers

Let ABCD and EDGF be parallelograms such that E is on AB and C is on GF, and the ratio

where x and y (with x ? y) are the lucky numbers of your pair.
Use GSP or GeoeGebra to construct a figure that fits the above descriptions.

Your construction should include the following steps. Marks will be deducted for using the wrong values of x and y and for missing steps.

(2)    Construct an arbitrary parallelogram ABCD (i.e., ABCD can change in shape and size by dragging but still remain as a parallelogram).

(3)    Construct the point E using dilation:
Using the Mark Center command in the Transform menu, mark A as the center of dilation.
Using the Dilate command in the Transform menu, dilate AB to AE by the fixed ratio x/(x + y).

(4)    Using the Distance command in the Measure menu, find the lengths |AE| and |AB|.
Using the Calculate command in the Measure menu, show that the ratio |AE| / |AB| is indeed x/(x + y). This ratio should remain the same after

dragging.

(5)    Construct the parallelogram EDGF that fits the given conditions. EDGF should remain as a parallelogram after dragging.

(6) Using the Quadrilateral Interior command in the Construct menu, construct the
interior of ABCD.
Using the Area command in the Measure menu, find the area of ABCD.

(7)    Similarly, find the area of EDGF. Check that area of ABCD = area of EDGF.

A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.