Introductory Modern Geometry of Point, Ray, and Circle |
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Page 70
... regular . 3. Show that this regular △ is equilateral . 4. One angle of a △ is a right - angle ; the others are equal ; how many degrees in each ? 5. One angle of a A is twice and the 70 GEOMETRY .
... regular . 3. Show that this regular △ is equilateral . 4. One angle of a △ is a right - angle ; the others are equal ; how many degrees in each ? 5. One angle of a A is twice and the 70 GEOMETRY .
Page 72
... regular ( i.e. equiangular and equilateral ) 3 - side , 4 - side , 5 - side , 8 - side , 12 - side . ( For proof that there is a regular n - side , see Art . 137. ) 16. Show that a ( convex ) polygon cannot have more than three obtuse ...
... regular ( i.e. equiangular and equilateral ) 3 - side , 4 - side , 5 - side , 8 - side , 12 - side . ( For proof that there is a regular n - side , see Art . 137. ) 16. Show that a ( convex ) polygon cannot have more than three obtuse ...
Page 74
... regular ? 34. A parallelogram is a rhombus if a diagonal bisects one of its angles . 35. A parallelogram is a square if its diagonals are equal and one bisects an angle of the parallelogram . 36. From any point in the base of an ...
... regular ? 34. A parallelogram is a rhombus if a diagonal bisects one of its angles . 35. A parallelogram is a square if its diagonals are equal and one bisects an angle of the parallelogram . 36. From any point in the base of an ...
Page 115
... . Theorem LXXVI . Proof . - There is a regular n - side . For the angle is a continuous magnitude ( why ? ) ; hence there are angles of all sizes from zero to a round I angle ; hence there is an angle , the TH . LXXVI . ] 115 THE CIRCLE .
... . Theorem LXXVI . Proof . - There is a regular n - side . For the angle is a continuous magnitude ( why ? ) ; hence there are angles of all sizes from zero to a round I angle ; hence there is an angle , the TH . LXXVI . ] 115 THE CIRCLE .
Page 117
... regular . Q. E. D. Corollary . The inner angle of a regular n - side is the -- n part of a straight angle . Find the value in degrees of the inner angles of the first ten regular n - sides . N.B. The foregoing demonstration merely ...
... regular . Q. E. D. Corollary . The inner angle of a regular n - side is the -- n part of a straight angle . Find the value in degrees of the inner angles of the first ten regular n - sides . N.B. The foregoing demonstration merely ...
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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.