Introductory Modern Geometry of Point, Ray, and Circle |
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Page 57
... diagonal . 74. Theorem XXXIII . Properties of the parallelogram . A. The opposite sides of a parallelogram are equal . This has just been proved . B ... diagonals of a parallelogram bisect each other ( TH . XXXIII . ] 57 PARALLELOGRAMS .
... diagonal . 74. Theorem XXXIII . Properties of the parallelogram . A. The opposite sides of a parallelogram are equal . This has just been proved . B ... diagonals of a parallelogram bisect each other ( TH . XXXIII . ] 57 PARALLELOGRAMS .
Page 58
William Benjamin Smith. D. The diagonals of a parallelogram bisect each other ( Fig . 47 ) A M The Proof . hence AM = FIG . 47 . AMB and CMD are congruent ( why ? ) ; CM , BM = DM . Q. E. D. 75. We may now convert all the foregoing ...
William Benjamin Smith. D. The diagonals of a parallelogram bisect each other ( Fig . 47 ) A M The Proof . hence AM = FIG . 47 . AMB and CMD are congruent ( why ? ) ; CM , BM = DM . Q. E. D. 75. We may now convert all the foregoing ...
Page 59
... diagonal into two congru- ent is a parallelogram . For the opposite angles must be equal ( why ? ) ; hence , etc. Q. E. D. D ' . A 4 - side whose diagonals bisect each other is a parallelogram . For the opposite sides are equal , being ...
... diagonal into two congru- ent is a parallelogram . For the opposite angles must be equal ( why ? ) ; hence , etc. Q. E. D. D ' . A 4 - side whose diagonals bisect each other is a parallelogram . For the opposite sides are equal , being ...
Page 60
... diagonals of a rhombus are nor- Let the student conduct the proof suggested by the figure ( Fig . 50 ) .女 FIG . 50 . Conversely , A parallelogram whose diagonals are normal to each other is equilateral , or a rhombus . Let the student ...
... diagonals of a rhombus are nor- Let the student conduct the proof suggested by the figure ( Fig . 50 ) .女 FIG . 50 . Conversely , A parallelogram whose diagonals are normal to each other is equilateral , or a rhombus . Let the student ...
Page 61
William Benjamin Smith. The diagonals of a rectangle are equal Theorem XXXVI . - ( Fig . 51 ) . A FIG . 51 . B For the AABC and BAD are congruent ( why ? ) ; hence AC = BD . Q. E. D. Conversely , A parallelogram with equal diagonals is ...
William Benjamin Smith. The diagonals of a rectangle are equal Theorem XXXVI . - ( Fig . 51 ) . A FIG . 51 . B For the AABC and BAD are congruent ( why ? ) ; hence AC = BD . Q. E. D. Conversely , A parallelogram with equal diagonals is ...
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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.