Introductory Modern Geometry of Point, Ray, and Circle |
From inside the book
Results 1-5 of 18
Page 36
... sides of the two △ coincide in pairs ( why ? Because through two points , as A ( A ' ) and B ( B ' ) , only one ray ... opposite to pairs of 48. Theorem XIV . - Two having two angles and the included side of the one equal respectively ...
... sides of the two △ coincide in pairs ( why ? Because through two points , as A ( A ' ) and B ( B ' ) , only one ray ... opposite to pairs of 48. Theorem XIV . - Two having two angles and the included side of the one equal respectively ...
Page 37
... sides , like APB , is called isosceles ; the third side is called the base , and its opposite angle the vertical angle . The angles at the base of an isosceles 50. Theorem XVI . △ are equal ; and conversely . Data : ABC an isosceles ...
... sides , like APB , is called isosceles ; the third side is called the base , and its opposite angle the vertical angle . The angles at the base of an isosceles 50. Theorem XVI . △ are equal ; and conversely . Data : ABC an isosceles ...
Page 38
... sides ( Fig . 30 ) . A A FIG . 30 . Α Proof . Take up the △ ABC , turn it ... opposite side is called the medial of that side . Corollary 1. In an ... opposite angle , the △ is isosceles . Can you prove it ? LOGICAL DIGRESSION . 51 ...
... sides ( Fig . 30 ) . A A FIG . 30 . Α Proof . Take up the △ ABC , turn it ... opposite side is called the medial of that side . Corollary 1. In an ... opposite angle , the △ is isosceles . Can you prove it ? LOGICAL DIGRESSION . 51 ...
Page 41
... opposite angles are unequal in the same sense ( i.e. the greater angle opposite the greater side ) ( Fig . 32 ) . R ... sides are unequal in the same sense . Proof . The opposite sides are not equal ; for when the sides are equal , the ...
... opposite angles are unequal in the same sense ( i.e. the greater angle opposite the greater side ) ( Fig . 32 ) . R ... sides are unequal in the same sense . Proof . The opposite sides are not equal ; for when the sides are equal , the ...
Page 46
... sides and an opposite angle in one equal to the two sides and the corresponding opposite angle in the a YC Α FIG . 37 . other . Let ABC and A'B'C ' ( Fig . 37 ) be the two A , with AB = A'B ' , BC = B'C ' , and angle a = angle a ' . Fit ...
... sides and an opposite angle in one equal to the two sides and the corresponding opposite angle in the a YC Α FIG . 37 . other . Let ABC and A'B'C ' ( Fig . 37 ) be the two A , with AB = A'B ' , BC = B'C ' , and angle a = angle a ' . Fit ...
Other editions - View all
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.