10. Through a given point draw a right line intersecting two given lines, and forming an isosceles triangle with them.
Def. i.—If two right lines in the same plane be such that, when produced indefinitely, they do not meet at any finite distance, they are said to be parallel.
Def. ii.—A parallelogram is a quadrilateral, both pairs of whose opposite sides are parallel.
Def. iii.—The right line joining either pair of opposite angles of a quadrilateral is called a diagonal.
Def. iv.—If both pairs of opposite sides of a quadrilateral be produced to meet, the right line joining their points of intersection is called its third diagonal.
Def. v.—A quadrilateral which has one pair of opposite sides parallel is called a trapezium.
Def. vi.—If from the extremities of one right line perpendiculars be drawn to another, the intercept between their feet is called the projection of the first line on the second.
Def. vii.—When a right line intersects two other right lines in two distinct points it makes with them eight angles, which have received special names in relation to one another. Thus, in the figure—1, 2; 7, 8 are called exterior angles; 3, 4; 5, 6, interior angles. Again, 4; 6; 3, 5 are called alternate angles; lastly, 1, 5; 2, 6; 3, 8; 4, 7 are called corresponding angles.