Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 13
... points is the middle point of the segment . It is also called the internal point of bisection of the seg- ment , or , when spoken of alone , simply the point of bisection . EXERCISES . I. If two segments be in line and have one common end- ...
... points is the middle point of the segment . It is also called the internal point of bisection of the seg- ment , or , when spoken of alone , simply the point of bisection . EXERCISES . I. If two segments be in line and have one common end- ...
Page 15
... point in the plane is said to rotate about the point . The point about which the rotation takes place is the pole , and ... middle one denotes the vertex , as LAOB . 3. The angle between two lines , when the vertex RELATIONS OF TWO LINES ...
... point in the plane is said to rotate about the point . The point about which the rotation takes place is the pole , and ... middle one denotes the vertex , as LAOB . 3. The angle between two lines , when the vertex RELATIONS OF TWO LINES ...
Page 20
... middle point is the right bisector of the segment . Since a segment has but one middle point ( 30 ° , Ex . 3 ) , and since but one perpendicular can be drawn to the segment through that point , .. a line - segment has but one right ...
... middle point is the right bisector of the segment . Since a segment has but one middle point ( 30 ° , Ex . 3 ) , and since but one perpendicular can be drawn to the segment through that point , .. a line - segment has but one right ...
Page 27
... point equidistant from the end- points of a line - segment is on the right bisector of that segment . ( Converse of 53 ... middle of the opposite side is a median of the triangle . Cor . 1. Every triangle has three medians . Cor . 2. The ...
... point equidistant from the end- points of a line - segment is on the right bisector of that segment . ( Converse of 53 ... middle of the opposite side is a median of the triangle . Cor . 1. Every triangle has three medians . Cor . 2. The ...
Page 32
... point and BC a line not pass- ing through it , and PA is to BC . I. PA which is to BC is shorter than any segment PB ... point in AC so that AD = AB . Then A is the middle point of BD , and PA is the right bisector of BD . .. and But ...
... point and BC a line not pass- ing through it , and PA is to BC . I. PA which is to BC is shorter than any segment PB ... point in AC so that AD = AB . Then A is the middle point of BD , and PA is the right bisector of BD . .. and But ...
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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