Supplementary angles. When the sum of two angles is equal to two right angles, each is called the supplement of the other, or is said to be supplementary to the other. (p. 66.) Parallel straight lines are straight lines in the same plane, which do not meet however far they are produced in either direction. Alternate angles, corresponding angles. See p. 70. (p. 70.) Triangle. A plane figure bounded by three straight lines is called a triangle. (p. 73.) Any side of a triangle may be taken as base. The line drawn perpendicular to the base from the opposite vertex is called the height, or altitude. (p. 172.) The straight line joining a vertex of a triangle to the mid-point of the opposite side is called a median. (p. 110.) Obtuse-angled triangle. A triangle which has one of its angles an obtuse angle is called an obtuse-angled triangle. (p. 81.) Right-angled triangle. A triangle which has one of its angles a right angle is called a right-angled triangle. The side opposite the right angle is called the hypotenuse. (p. 81.) Acute-angled triangle. A triangle which has all its angles acute is called an acute-angled triangle. (p. 82.) Isosceles triangle. A triangle which has two of its sides equal is called an isosceles triangle. (p. 82.) Equilateral triangle. A triangle which has all its sides equal is called an equilateral triangle. (p. 82.) Scalene triangle. A triangle which has no two of its sides equal is called a scalene triangle. (p. 82.) Quadrilateral. A plane figure bounded by four straight lines is called a quadrilateral. (p. 73.) The straight lines which join opposite corners of a quadrilateral are called its diagonals. (p. 73.) Parallelogram. A quadrilateral with its opposite sides parallel is called a parallelogram. (p. 73.) Any side of a parallelogram may be taken as the base. The perpendicular distance between the base and the opposite (parallel) side is called the height, or altitude. (p. 167.) Rectangle. A parallelogram which has one of its angles a right angle is called a rectangle. (p. 135.) Square. A rectangle which has two adjacent sides equal is called a square. (p. 135.) Rhombus. A parallelogram which has two adjacent sides equal is called a rhombus. (p. 135.) Trapezium. A quadrilateral which has only one pair of sides parallel is called a trapezium. A trapezium in which the sides that are not parallel are equal is called an isosceles trapezium. (p. 135.) Polygon. A plane figure bounded by straight lines is called a polygon, or, a rectilinear figure. (p. 83.) Regular polygon. A polygon which has all its sides equal and all its angles equal is called a regular polygon. (p. 84.) Pentagon, hexagon, heptagon, octagon, etc.-a polygon of 5, 6, 7, 8, ... sides; 5-gon, 6-gon, 7-gon, 8-gon.... (p. 18.) Vertices. The corners of a triangle or polygon are called its vertices. (p. 16.) Perimeter. The perimeter of a figure is the sum of its sides. (p. 18.) Tetrahedron, pyramid, net. (See pp. 26-27.) Cube, cuboid, prism, wedge. (See pp. 42-44.) Cylinder, cone, sphere. (See p. 217.) Locus. If a point moves so as to satisfy certain conditions, the path traced out by the point is called its locus. (p. 144.) Envelope. If a line moves so as to satisfy certain conditions, the curve which its different positions mark out is called its envelope. Projection. (See p. 210.) Circle. A circle is a line, lying in a plane, such that all points in the line are equidistant from a certain fixed point, called the centre of the circle. The fixed distance is called the radius of the circle. (p. 217.) Circumference, chord, major and minor arc, segment, sector, semicircle. (See pp. 217-219.) Tangent. A tangent to a circle is a straight line which, however far it may be produced, has one point, and one only, in common with the circle. The tangent is said to touch the circle; the common point is called the point of contact. (p. 238.) Inscribed polygon. If a circle passes through all the vertices of a polygon, the circle is said to be circumscribed about the polygon; and the polygon is said to be inscribed in the circle. (p. 224.) Circumscribed polygon. If a circle touches all the sides of a polygon, it is said to be inscribed in the polygon; and the polygon is said to be circumscribed about the circle. (p. 224.) Circumcentre. The centre of a circle circumscribed about a triangle is called the circumcentre of the triangle. (p. 224.) Escribed circles of a triangle. (See p. 244.) Contact of circles. If two circles touch the same line at the same point, they are said to touch one another. (p. 245.) Angle in a segment. An angle in a segment of a circle is the angle subtended by the chord of the segment at a point on the arc. (p. 253.) Major segment, minor segment. (See p. 253.) Concyclic. Points which lie on the same circle are said to be concyclic. (p. 257.) Cyclic quadrilateral. If a quadrilateral is such that a circle can be circumscribed about it, the quadrilateral is said to be cyclic. (p. 261.) Common tangents, exterior and interior. (See p. 263.) Symmetry. (See p. 51.) Congruent. Figures which are equal in all respects are said to be congruent. (p. 85.) Equivalent. Figures which are equal in area are said to be equivalent. (p. 168.) Similar. Figures which are equiangular to one another and have their corresponding sides proportional are said to be similar. (p. 313.) Ratio, Proportion. (See pp. 302, 303.) Fourth proportional. If x is such a magnitude that a:b=c:x, then x is called the fourth proportional to the three magnitudes a, b, c. (p. 309.) Third proportional. If x is such a magnitude that a:b=b: x, then æ is called the third proportional to the two magnitudes a, b. (p. 309.) Mean proportional. If x is such a magnitude that a:x=x:b, then x is called the mean proportional between a and b. (p. 331.) |