(7) To construct a scalene triangle ABC, the lengths of the sides of which are given.

Measure off and draw the base BC. With centre B and distance equal to one of the given sides describe an arc. With centre C and distance equal to the remaining side make an arc to intersect the first arc in A. Join AB, AC.

A scalene triangle has all its sides unequal.

We can draw four equal scalene triangles on the same base, first by reversing the order of the sides above the line, and then by drawing below the base triangles equal to those above it.

(8) To construct a triangle ABC when the angle ABC is given and the lengths of BA and BC.

Measure off the lengths BA and BC along the straight lines BA and BC. Join AC.

(9) To describe a square upon a given straight line AB.

At the point A draw a straight line AD perpendicular to AB and equal to it (see page 14, fig. 19). With centres B and D, and distances each equal to AB make arcs to intersect in C. Join BC and DC.

A square is a four sided rectilineal figure, having all its sides equal, and its angles right angles.

(10) To describe a rhombus ABCD having given a diagonal AC and the length of one of its sides AB.

Describe on the base AC two isosceles triangles (page 4) ABC, and ADC, one on one side and one on the other side of the base.

A rhombus is a quadrilateral rectilineal figure that has all its sides equal, but its angles are not right angles.

(11) To describe a rhombus ABCD when the angle ABC is given and one of its sides.

Draw the angle ABC included by the two straight lines AB, BC each of length equal to the given side.

With centres A and C and distances each equal to the given side make arcs intersecting in D.

Join AD, CD.

The diagonals of rhombus AC, BD intersect at right angles at K and bisect one another (fig. 17).

(12) To construct a parallelogram EFGH having given the lengths of the diagonal HF and the sides HE, EF.

Construct the two scalene triangles HEF and FGH above and below the base HF where FG HE and GH

=

FE.

A parallelogram is sometimes called a rhomboid.

(13) To construct a parallelogram EFGH having given one angle EHG and the lengths of the sides HE, HG.

=

With centre E make an arc at distance centre G make an arc to intersect it at distance the first arc in F. Join EF, FG.

HG, and with = HE to meet

(14) To construct a rectangle EFGH having given the two sides.

Make a right angle EHG, measure off the sides HE and HG, and proceed as in the last example.

A rectangle or oblong is a right-angled parallelogram. (15) Through a given point E to draw a parallel to a given straight line HG.

With centre E and any convenient distance make an arc to meet HG in H, with the same distance mark off HG, and still keeping the same distance mark off arcs from centres E and G. Join EF, the line required.

The construction for the rhombus has here been used, that for a parallelogram will do equally well.

(16) To describe a square ABCD, the diagonal AC being of given length.

Draw two straight lines AC, BD at right angles intersecting in K. Measure KA, KB, KC, KD each equal to half the given length of the diagonal. Join AB, BC, CD, DA.

(17) To describe a rhombus ABCD where the lengths of the diagonals AC, BD are known.

K.

Draw two straight lines AC, BD at right angles meeting in Measure KA, and KC each equal to half of one diagonal,` and KB, KD each equal to half of the other diagonal. Join AB, BC, CD, DA.

(18) To construct a rectilineal figure of any number of sides, such as ABCDE where the lengths of its sides and diagonals are given.

First construct the triangle ABC; then on the base AC describe the triangle ACD; next on AD describe ADE, and

so on.