Introductory Modern Geometry of Point, Ray, and Circle |
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Page 57
... parallelogram , and may be denoted by the symbol . A join of opposite vertices , as BD , is called a diagonal . 74. Theorem XXXIII . Properties of the parallelogram ... parallelogram bisect each other ( TH . XXXIII . ] 57 PARALLELOGRAMS .
... parallelogram , and may be denoted by the symbol . A join of opposite vertices , as BD , is called a diagonal . 74. Theorem XXXIII . Properties of the parallelogram ... parallelogram bisect each other ( TH . XXXIII . ] 57 PARALLELOGRAMS .
Page 58
... parallelogram . Theorem XXXIV . — A ' . A 4 - side with its opposite sides equal is a parallelogram . Data : ABCD , AD = CB ( Fig 48 ) . A B FIG . 48 . Proof . Draw BD . Then ABD and CDB are congruent ( why ? ) ; hence B = 8 ; and AD ...
... parallelogram . Theorem XXXIV . — A ' . A 4 - side with its opposite sides equal is a parallelogram . Data : ABCD , AD = CB ( Fig 48 ) . A B FIG . 48 . Proof . Draw BD . Then ABD and CDB are congruent ( why ? ) ; hence B = 8 ; and AD ...
Page 59
... parallelogram . Q. E. D. C ' . A 4 - side that is cut by each 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 ...
... parallelogram . Q. E. D. C ' . A 4 - side that is cut by each 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 ...
Page 60
... parallelogram is a 4 - side with opposite angles equal ; and conversely , every 4 - side with opposite angles equal is a parallelogram . Not every property is definitive , and hence not every property may be used as test or criterion ...
... parallelogram is a 4 - side with opposite angles equal ; and conversely , every 4 - side with opposite angles equal is a parallelogram . Not every property is definitive , and hence not every property may be used as test or criterion ...
Page 61
... parallelogram with equal diagonals is equi- angular , or a rectangle . For the AABC and BAD are again congruent , though for another reason . What reason ? 79. Def . A parallelogram both equilateral and equi- angular is called a square ...
... parallelogram with equal diagonals is equi- angular , or a rectangle . For the AABC and BAD are again congruent , though for another reason . What reason ? 79. Def . A parallelogram both equilateral and equi- angular is called a square ...
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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.