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NOTE.-Angle ABC is a right angle, and the lines drawn from A and C to any point in the arc of the semicircle would form a right angle (Euc. III., 31).
To construct a rhombus, its side AB and one diagonal AC being given.
1. With centres A and C, and radius AB, describe arcs
cutting at D and B. 2. Join AD, DC, CB, and BA. Then ADCB is the rhombus
To construct a rhombus, its side AB and an angle C being given.
1. Make angle BAD equal to C (Pr. 10), and cut off AE.
equal to AB.
intercepting in the point F.
To construct a rhomboid, its two adjacent sides AB and BC, and a diagonal AC, being given.
1. From A in AB, with the diagonal AC as radius, describe
2. From B, with radius BC, cut the arc in C.
To construct a rhomboid, its two adjacent sides AB and BC, and angle D being given.
1. At A in AB make the angle BAF equal to the given
angle D (Pr. 10), and cut off AE equal to BC.
B 2. From B, with radius BC, describe an arc above B. 3. From E as centre, with radius AB, cut the arc in C. 4. Join EC and CB. Then A ECB is the required rhomboid.
1. Make line EF equal to CD, and the angle at E equal to
the angle at D (Pr. 10).
3. From the point G, with radius AB, and from F, with
radius BC, describe arcs cutting in H. 4. Join GH, FH. Then the trapezium EFGH shall be equal
to the given trapezium ABCD.
To construct a trapezium, having its adjacent pairs of sides equal respectively to two given lines AB and CD, and its diagonal equal to the given line EF.
1. From centre E, with AB radius, and from centre F, with
CD radius, describe arcs cutting in G and H. 2. Join EG, GF, FH, and HE. Then EGFH is the required
To construct a trapezium when the length of the diagonal AB, and the angles at its extremities A and B are given.
1. Make any straight line CD equal to the diagonal AB.
2. Make angles at C equal and correspondent to the angles
at A ; and angles at D equal and correspondent to the
angles at B (Pr. 10). 3. Produce their sides until they meet. Then the figure
CEDF is the required trapezium.