Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 44
... quadrangle or quadrilateral . Thus ABCD is a quadrangle . 2. The line - segments AC and BD which join opposite vertices are the diagonals of the quadrangle . 3. The quadrangle formed when two parallel lines intersect two 44 SYNTHETIC ...
... quadrangle or quadrilateral . Thus ABCD is a quadrangle . 2. The line - segments AC and BD which join opposite vertices are the diagonals of the quadrangle . 3. The quadrangle formed when two parallel lines intersect two 44 SYNTHETIC ...
Page 45
Nathan Fellowes Dupuis. 3. The quadrangle formed when two parallel lines intersect two other parallel lines is a parallelogram , and is usually denoted by the symbol J. 81 ° . Theorem . - In any parallelogram- 1. The opposite sides are ...
Nathan Fellowes Dupuis. 3. The quadrangle formed when two parallel lines intersect two other parallel lines is a parallelogram , and is usually denoted by the symbol J. 81 ° . Theorem . - In any parallelogram- 1. The opposite sides are ...
Page 46
... . ABDG = AFDH , ( 64 ° ) and BD = DF . g.e.d. Def . - The figure ABFE is a trapezoid . Therefore a trapezoid is a quadrangle having only two sides parallel . The parallel sides are the major and 46 SYNTHETIC GEOMETRY .
... . ABDG = AFDH , ( 64 ° ) and BD = DF . g.e.d. Def . - The figure ABFE is a trapezoid . Therefore a trapezoid is a quadrangle having only two sides parallel . The parallel sides are the major and 46 SYNTHETIC GEOMETRY .
Page 50
... quadrangle will mean this figure . 2. The quadrangle ( 2 ) in which one of the internal angles , as at D , is greater than a straight angle . Such an angle in a closed figure is called a re - entrant angle . We will call this an ...
... quadrangle will mean this figure . 2. The quadrangle ( 2 ) in which one of the internal angles , as at D , is greater than a straight angle . Such an angle in a closed figure is called a re - entrant angle . We will call this an ...
Page 51
... quadrangle , and the ( hyp . ) ( 90 ° ) ( 39 ° ) But LBCD is supplementary to △ BAD . LBCD is supplementary to LECD ; and the ( BC . CD ) is either the angle BCD or DCE . 4 ( BC . CD ) is = or supplementary to BAD . q.e.d. EXERCISES ...
... quadrangle , and the ( hyp . ) ( 90 ° ) ( 39 ° ) But LBCD is supplementary to △ BAD . LBCD is supplementary to LECD ; and the ( BC . CD ) is either the angle BCD or DCE . 4 ( BC . CD ) is = or supplementary to BAD . q.e.d. EXERCISES ...
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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