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PROP. VII. THEOR.
On the same base, and on the same side of it,
there cannot be two triangles having their conterminous sides at both extremities of the base, equal to each other.
PROP. VIII. THEOR.
If two triangles have two sides of the one re
spectively equal to two sides of the other, and also their bases equal; then the angles contained by their equal sides are also equal.
PROP. XII. PROB.
To draw a straight line perpendicular to a given
indefinite straight line from a given point without.
PROP. XIII. THEOR.
When a straight line standing upon another
straight line makes angles with it; they are either two right angles, or together equal to two right angles.
Cor.—Since the angles made at any point on one side of a straight line, are equal to two right angles ; it is manifest that the angles at any point in a straight line, on both sides of it, or all the angles round a point, are together equal to four right angles.
PROP. XIV. THEOR. If two straight lines, meeting a third straight
line, at the same point, and at opposite sides of it, make with it the adjacent angles equal to two right angles; these straight lines lie in one continuous straight line.
PROP. XV. THEOR. Where two straight lines intersect each other,
the vertically opposite angles made by them are equal.
PROP. XVI. THEOR. If a side of a triangle is produced, the external
angle is greater than either of the internal remote angles.