Introductory Modern Geometry of Point, Ray, and Circle |
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Page 35
... join them in pairs by rays ; and since there are three pairs , BC , CA , AB , then there are three rays , which we may name L , M , N. Thus we see that three points determine three rays , just as three rays determine three points . This ...
... join them in pairs by rays ; and since there are three pairs , BC , CA , AB , then there are three rays , which we may name L , M , N. Thus we see that three points determine three rays , just as three rays determine three points . This ...
Page 41
... Join BB ' ; then AR is the mid - normal of BB ' ( why ? ) , and hence angle CBB ' = angle BB'R ( why ? ) . Hence angle BB'C > B'BC ( why ? ) ; hence BC > B'C ( why ? ) . B'CAC - AB ; hence BC > AC - AB ; i.e. But Theorem XIX . - Any ...
... Join BB ' ; then AR is the mid - normal of BB ' ( why ? ) , and hence angle CBB ' = angle BB'R ( why ? ) . Hence angle BB'C > B'BC ( why ? ) ; hence BC > B'C ( why ? ) . B'CAC - AB ; hence BC > AC - AB ; i.e. But Theorem XIX . - Any ...
Page 57
... join of opposite vertices , as BD , is called a diagonal . 74. Theorem XXXIII . Properties of the parallelogram . A. The opposite sides of a parallelogram are equal . This has just been proved . B. The opposite angles of a parallelogram ...
... join of opposite vertices , as BD , is called a diagonal . 74. Theorem XXXIII . Properties of the parallelogram . A. The opposite sides of a parallelogram are equal . This has just been proved . B. The opposite angles of a parallelogram ...
Page 71
... joining consecutively any number of points ( first with second , second with third , etc. ) is called a broken line , or train of tracts , or polygon . Where the last point falls on the first the polygon is closed ; EXERCISES I. 71.
... joining consecutively any number of points ( first with second , second with third , etc. ) is called a broken line , or train of tracts , or polygon . Where the last point falls on the first the polygon is closed ; EXERCISES I. 71.
Page 73
... joins of the consecutive mid - points of the sides of a 4 - side form a parallelogram . 31. The joins of the mid - points of the pairs of opposite sides and of the pairs of diagonals of a 4 - side concur , bisect- ing each other . 32 ...
... joins of the consecutive mid - points of the sides of a 4 - side form a parallelogram . 31. The joins of the mid - points of the pairs of opposite sides and of the pairs of diagonals of a 4 - side concur , bisect- ing each other . 32 ...
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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.