Introductory Modern Geometry of Point, Ray, and Circle |
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Page 19
... arms . When we would distinguish these arms as beginning and end , we mention the letter on the beginning- arm first , and the letter on the end - arm last ; thus , AOB ; here OA is the beginning and OB the end of the angle . Exchanging ...
... arms . When we would distinguish these arms as beginning and end , we mention the letter on the beginning- arm first , and the letter on the end - arm last ; thus , AOB ; here OA is the beginning and OB the end of the angle . Exchanging ...
Page 30
... ( Fig . 22 ) form four angles a , ẞ , a ' , B ' . Two angles , as « and ẞ , that have a common arm , are called adjacent . Accordingly we see at once : Theorem VIII . -Where two rays intersect , the sum 30 [ TH . VII . GEOMETRY .
... ( Fig . 22 ) form four angles a , ẞ , a ' , B ' . Two angles , as « and ẞ , that have a common arm , are called adjacent . Accordingly we see at once : Theorem VIII . -Where two rays intersect , the sum 30 [ TH . VII . GEOMETRY .
Page 31
... arms of the one being counter to the arms of the other , are called opposite , or vertical , or counter . Theorem IX . - When two rays meet , the opposite angles formed are equal . For a ( why ? ) . + BS ( a straight angle ) ( why ...
... arms of the one being counter to the arms of the other , are called opposite , or vertical , or counter . Theorem IX . - When two rays meet , the opposite angles formed are equal . For a ( why ? ) . + BS ( a straight angle ) ( why ...
Page 33
... arms of the angle , is called the inner Bisector or mid - ray of the angle . The inner bisector of an adjacent supplemental angle is called the outer bisector of the angle itself . Thus OI bisects innerly and OE bisects outerly the ...
... arms of the angle , is called the inner Bisector or mid - ray of the angle . The inner bisector of an adjacent supplemental angle is called the outer bisector of the angle itself . Thus OI bisects innerly and OE bisects outerly the ...
Page 100
... arms passing through the ends of that arc , is said to be inscribed in that arc . Hence for an angle to be inscribed in a certain arc , and for it to stand on the explemental arc , are equivalent . Corollary 2. All angles inscribed in ...
... arms passing through the ends of that arc , is said to be inscribed in that arc . Hence for an angle to be inscribed in a certain arc , and for it to stand on the explemental arc , are equivalent . Corollary 2. All angles inscribed in ...
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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.