Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 4
... ( corresponds to or is opposite ) Y , therefore Y is ( corresponds to or is opposite ) X. 8 ° . A Corollary is a theorem deduced from some other theorem , usually by some qualification or restriction , and occasionally by some ...
... ( corresponds to or is opposite ) Y , therefore Y is ( corresponds to or is opposite ) X. 8 ° . A Corollary is a theorem deduced from some other theorem , usually by some qualification or restriction , and occasionally by some ...
Page 26
... corresponding parts in the other . 53 ° . Theorem . - Every point upon the right bisector of a segment is equidistant from the end - points of the segment . AB is a line - segment , and P is any point on its right bisector PC . Then PA ...
... corresponding parts in the other . 53 ° . Theorem . - Every point upon the right bisector of a segment is equidistant from the end - points of the segment . AB is a line - segment , and P is any point on its right bisector PC . Then PA ...
Page 35
... corresponding parts in the other . But in order to establish the congruence of two triangles it is not necessary to establish independently the respective equality of all the parts ; for , as has now been shown , if certain of the ...
... corresponding parts in the other . But in order to establish the congruence of two triangles it is not necessary to establish independently the respective equality of all the parts ; for , as has now been shown , if certain of the ...
Page 36
... corresponding angle in the other . This is known as the ambiguous case in the solution of triangles . A study of the preceding table shows that a triangle is completely given when any three of its six parts are given , with two ...
... corresponding angle in the other . This is known as the ambiguous case in the solution of triangles . A study of the preceding table shows that a triangle is completely given when any three of its six parts are given , with two ...
Page 41
... corresponding angles . c and f , e and d are pairs of alternate angles . c and e , d and fare pairs of interadjacent angles . 74 ° . When a transversal crosses parallel lines- 1. The alternate angles are equal in pairs . 2. The ...
... corresponding angles . c and f , e and d are pairs of alternate angles . c and e , d and fare pairs of interadjacent angles . 74 ° . When a transversal crosses parallel lines- 1. The alternate angles are equal in pairs . 2. The ...
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Common terms and phrases
ABCD Algebra altitude becomes bisects c.p.-circles centre of similitude chord of contact circles touch circumcircle co-axal coincide collinear concurrent concurrent lines concyclic congruent cut the circle denote diagonals diameter divided double points end-points equal angles equianharmonic equilateral triangle excircles external bisector fixed point geometric given circles given line given point harmonic range Hence hexagram homographic homologous hypothenuse incircle internal angles inverse points isosceles joins LAOB line-segment locus median middle point nine-points circle opposite sides orthogonally pair parallel parallelogram passes pencil perpendicular perspective plane point of contact point of intersection polar reciprocal Proof quadrangle radical axis radical centre radii radius rectangle rectilinear figure regular polygon rhombus right angle right bisector rotation secant similar Similarly square straight angle symbol tangent tensor theorem Theorem.-The three circles transversal vertex vertices