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each other in C and D, and lines be drawn joining A and B to C and D, the figure ACBD will be the required rhombus. Problem 17 (Fig. 64). To construct a rhomboid, the lengths of two adjacent sides and one of a pair of its opposite angles being given. Let AB be one (the longest) of the adjacent sides, and E one of the opposite angles. At A make the angle CAB equal to the angle E, and cut off AC equal to the shorter adjacent side. From C, with AB as radius, describe an arc, and from B, with AC as radius, describe another cutting the first in D, join ACDB, and it is the required rhomboid. If a diagonal AB (Fig. 65) and the lengths of two adjacent sides be given : Then, with the length of one of those sides as a radius, and from A and B as centres, describe arcs on opposite sides of AB, and from the same centres, with the length of the other adjacent side as radius, describe arcs cutting those first drawn in C and D, join AC, CB,BD,DA, and it will be the required rhomboid. Problem 18 (Fig. 66). To construct a trapezium, the length of its sides and one of its angles being given. Let AB be the base of the figure or side on which it stands, and C the given angle. At A in AB make DAB equal to the angle C, and let AD equal the length of that side of the figure ; with the length of the opposite side as radius, and from B as centre, describe an arc, and from D as centre, with the length of the fourth side as radius, strike an arc cutting the last in E, join ADEB, and the required trapezium is constructed. 14. In the construction of the preceding plane figures, the lengths of one or more of their sides, with their relation to each other, are previously known or determined by the given problem. In the case of