Introductory Modern Geometry of Point, Ray, and Circle |
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Page 16
... correspond . It is manifest that all planes are congruent and all rays are congruent . Rays and planes are unbounded , but whether or not they are finite is a question that we are unable to answer . 16. Any part of a circle or ray , as ...
... correspond . It is manifest that all planes are congruent and all rays are congruent . Rays and planes are unbounded , but whether or not they are finite is a question that we are unable to answer . 16. Any part of a circle or ray , as ...
Page 46
... corresponding opposite angle in the a YC Α FIG . 37 . other . Let ABC and A'B'C ' ( Fig . 37 ) be the two A , with AB = A'B ' , BC = B'C ' , and angle a = angle a ' . Fit a ' on a ; then A'B ' falls on AB , B 46 [ TH . XXIV . GEOMETRY .
... corresponding opposite angle in the a YC Α FIG . 37 . other . Let ABC and A'B'C ' ( Fig . 37 ) be the two A , with AB = A'B ' , BC = B'C ' , and angle a = angle a ' . Fit a ' on a ; then A'B ' falls on AB , B 46 [ TH . XXIV . GEOMETRY .
Page 47
... corresponding part of the other are congruent . B AA D FIG . 38 . 62. We have seen ( Art . 47 ) that when two △ have two sides and included angle in one equal to two sides and included angle in the other , they are congruent . TH . XXV ...
... corresponding part of the other are congruent . B AA D FIG . 38 . 62. We have seen ( Art . 47 ) that when two △ have two sides and included angle in one equal to two sides and included angle in the other , they are congruent . TH . XXV ...
Page 53
... Bla T Μ ́ = α . L B M a Y / S FIG . 44 . Then plainly B ' = ß , This is evidently possible ( why ? ) . y ' = y , d ' = 8 , α ' = a ; they are called corresponding angles ; - also a and y ' , ẞ and d TH . XXX . ] 53 TRIANGLES .
... Bla T Μ ́ = α . L B M a Y / S FIG . 44 . Then plainly B ' = ß , This is evidently possible ( why ? ) . y ' = y , d ' = 8 , α ' = a ; they are called corresponding angles ; - also a and y ' , ẞ and d TH . XXX . ] 53 TRIANGLES .
Page 54
... corresponding angles equal , or a pair of alternate angles equal , or a pair of interadjacent angles supplemental , are non - intersectors . 70. But another query now arises . Is it possible to draw another ray through O ' so close to L ...
... corresponding angles equal , or a pair of alternate angles equal , or a pair of interadjacent angles supplemental , are non - intersectors . 70. But another query now arises . Is it possible to draw another ray through O ' so close to L ...
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Common terms and phrases
adjacent angles altitudes angle AOB angles equal anti-parallelogram axal symmetry Axiom axis of symmetry bisect called central angle central symmetry centre of symmetry chord circle K circles touch circumcircle concur congruent construction conversely Corollary corresponding angles curve Data diagonals diameter dimensions distance draw a circle Draw a ray drawn Elementary Algebra ends equal angles falls figure film fixed point Geometry given angle given point given ray half-rays halves homœoidal included angle inner angles inner mid-rays innerly intercept intersection isosceles join kite Let the student locus medial meet mid-points normal opposite angles opposite sides outer angle pairs parallel parallelogram plane point equidistant point of touch polygon position Problem Proof proposition radii radius reciprocal regular n-side reversible rhombus right angle round angle secant Solution Space sphere-surface straight angle subtended surface symmetric tangent tangent-lengths Theorem unequal vertex vertices
Popular passages
Page 95 - A circle is a closed plane curve, all points of which are equidistant from a point within called the center.
Page 35 - Two parallelograms, having two sides and the included angle of the one equal respectively to two sides and the included angle of the other, are equal.
Page 43 - BDN, have the three sides of the one equal respectively to the three sides of the other...
Page 70 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.