## Theoretical Geometry: Based on the Various Geometry Books by Godfrey and Siddons |

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### Common terms and phrases

altitude base BC bisector bisects called centre chord circle circles touch circumference circumscribed congruent constant Constr Construction CONVERSE corresponding Data ABC described diagonals diameter distance divided draw drawn drawn parallel edges equal equiangular equidistant equilateral triangle equivalent externally falls figure formed four Geometry given given point Hence inscribed inside internally intersect isosceles triangle Join length line drawn line joining locus mean measured meet mid-point NOTE opposite sides pair parallel parallel to BC parallelogram pass perpendicular polygon produced Proof proportional Prove quadrilateral ABCD radii radius ratio regular respectively right angles segment Show similar square straight line subtends taken tangent THEOREM triangle ABC units vertex vertices

### Popular passages

Page 20 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Page 46 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 29 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page vii - When a straight line cuts two other straight lines, if (i) a pair of alternate angles are equal, or (ii) a pair of corresponding angles are equal, or (iii) a pair of interior angles on the same side of the cutting line are together equal to two right angles, then the two straight lines are parallel ; and the converse.

Page 62 - If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts.

Page 76 - A straight line, drawn from the centre of a circle to bisect a chord which is not a diameter, is at right angles to the chord ; conversely, the perpendicular to a chord from the centre bisects the chord. There is one circle, and one only, which passes through three given points not in a straight line. In equal circles (or, in the same circle) (i) if two...

Page xiv - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.

Page 70 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.

Page 59 - In a right-angled triangle the square on the side subtending the right angle is equal to the sum of the squares on the sides containing the right angle.

Page 92 - Angles in the same segment of a circle are equal; and. if the line joining two points subtends equal angles at two other points on the same side of it, the four points lie on a circle.