Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 17
... therefore the sum of each pair is a straight angle ( 36 ° ) . q.e.d. Cor . 1. The angle between the opposite directions of a line is a straight angle . B Cor . 2. If a radius vector be rotated until RELATIONS OF TWO LINES . - ANGLES . 17.
... therefore the sum of each pair is a straight angle ( 36 ° ) . q.e.d. Cor . 1. The angle between the opposite directions of a line is a straight angle . B Cor . 2. If a radius vector be rotated until RELATIONS OF TWO LINES . - ANGLES . 17.
Page 18
... pairs of opposite or vertical angles , viz . , A , A ' , and B , B ' , A being opposite A ' , and B being opposite B ' . 40 ° . Theorem . - The opposite angles of a pair formed by two intersecting lines are equal to one another . Proof ...
... pairs of opposite or vertical angles , viz . , A , A ' , and B , B ' , A being opposite A ' , and B being opposite B ' . 40 ° . Theorem . - The opposite angles of a pair formed by two intersecting lines are equal to one another . Proof ...
Page 19
... pairs . But if any one of these is a right angle , all four are right angles . Perpendicularity is the most important directional relation in the applications of Geometry . Def . 4. - An acute angle is less than a right angle , and an ...
... pairs . But if any one of these is a right angle , all four are right angles . Perpendicularity is the most important directional relation in the applications of Geometry . Def . 4. - An acute angle is less than a right angle , and an ...
Page 41
... pairs of corresponding angles . c and f , e and d are pairs of alternate angles . c and e , d and fare pairs of ... pair of interadjacent angles is a straight angle . AB is to CD and EF is a transversal . A J. LAEF LEFD . Proof ...
... pairs of corresponding angles . c and f , e and d are pairs of alternate angles . c and e , d and fare pairs of ... pair of interadjacent angles is a straight angle . AB is to CD and EF is a transversal . A J. LAEF LEFD . Proof ...
Page 42
... pairs . 3. LAEF + 2CFE = 1 . Proof.- and LAEF = LEFD , LCFE + LEFD = 1 ; LAEF + 4CFE = 1 . ( 74 ° , 1 ) ( 38 ° ) q.e.d. Cor . It is seen from the theorem that the equality of a pair of alternate angles determines the equality in pairs ...
... pairs . 3. LAEF + 2CFE = 1 . Proof.- and LAEF = LEFD , LCFE + LEFD = 1 ; LAEF + 4CFE = 1 . ( 74 ° , 1 ) ( 38 ° ) q.e.d. Cor . It is seen from the theorem that the equality of a pair of alternate angles determines the equality in pairs ...
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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