Elementary Synthetic Geometry of the Point, Line and Circle in the Plane |
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Page 24
... base , and then the angles at the extremities of the base are its basal angles , and the angle opposite the base is the vertical angle . The vertex of the vertical angle is the vertex of the triangle when spoken of in relation to the ...
... base , and then the angles at the extremities of the base are its basal angles , and the angle opposite the base is the vertical angle . The vertex of the vertical angle is the vertex of the triangle when spoken of in relation to the ...
Page 26
... base . Cor . 1. Since the △ APC = ^ \ BPC , .. LA = LB . Hence the basal angles of an isosceles triangle are equal to one another . Cor . 2. From ( 52 ° , Cor . ) , LAPC = 2BPC ; Therefore the right bisector of the base of an isosceles ...
... base . Cor . 1. Since the △ APC = ^ \ BPC , .. LA = LB . Hence the basal angles of an isosceles triangle are equal to one another . Cor . 2. From ( 52 ° , Cor . ) , LAPC = 2BPC ; Therefore the right bisector of the base of an isosceles ...
Page 27
... base , all the angles of an equilateral triangle are equal to one another ; or , an equilateral triangle is ... base of an isosceles triangle is the right bisector of the base , and the internal THREE OR MORE POINTS AND LINES . 27.
... base , all the angles of an equilateral triangle are equal to one another ; or , an equilateral triangle is ... base of an isosceles triangle is the right bisector of the base , and the internal THREE OR MORE POINTS AND LINES . 27.
Page 28
Nathan Fellowes Dupuis. the right bisector of the base , and the internal bisector of the vertical angle . ( 53 ° , Cor . 2. ) Cor . 3. The three medians of an equilateral triangle are the three right bisectors of the sides , and the ...
Nathan Fellowes Dupuis. the right bisector of the base , and the internal bisector of the vertical angle . ( 53 ° , Cor . 2. ) Cor . 3. The three medians of an equilateral triangle are the three right bisectors of the sides , and the ...
Page 47
Nathan Fellowes Dupuis. sides parallel . The parallel sides are the major and minor bases of the figure . Cor . 1 ... base EF ' . E D Therefore , I , the line through the middle point of one side of a triangle , parallel to a second ...
Nathan Fellowes Dupuis. sides parallel . The parallel sides are the major and minor bases of the figure . Cor . 1 ... base EF ' . E D Therefore , I , the line through the middle point of one side of a triangle , parallel to a second ...
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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