Question

Use a reflection to construct (with the ruler and compass) a quadrilateral given all the side lengths (a,b,c,d) and the fact that a given diagonal bisects an angle (say the one formed by the sides a and b).

Answer 1

Firstly, draw a vertical line. Now let the quadrilateral be ABCD. Mark a point A on the vertical line, and draw the line AB of length 'a' at any given angle, using a compass, to the vertical line. Measure the angle using a protractor . Now, draw a perpendicular from the point B onto the vertical line and extend . Use your compass to draw the same angle on the other side of the vertical line. The point where the perpendicular intersects with the angle drawn, mark it as point D. Measure the length 'c' and keeping your compass needle at D, cut out length 'c' on the vertical line.Name it point C. Then connect points B and C. Hence the quadrilateral is complete.