The Essentials of Geometry (plane) |
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Page 4
... angle . , angles . S , parallelograms . O , circle . , circles . The following abbreviations will also be used : Ax ... Exterior . Rt . , Right . Corresp . , Corresponding . Str . , Straight . Rect . , Rectangle , rec- Adj ...
... angle . , angles . S , parallelograms . O , circle . , circles . The following abbreviations will also be used : Ax ... Exterior . Rt . , Right . Corresp . , Corresponding . Str . , Straight . Rect . , Rectangle , rec- Adj ...
Page 9
... angles have their exterior sides in the same straight line , their sum is equal to two right angles . E A C B Let angles ACD and BCD have their sides AC and BC in the same straight line . To prove the sum of angles ACD and BCD equal to ...
... angles have their exterior sides in the same straight line , their sum is equal to two right angles . E A C B Let angles ACD and BCD have their sides AC and BC in the same straight line . To prove the sum of angles ACD and BCD equal to ...
Page 23
... angles of the triangle are the B angles CAB , ABC , and BCA , included between the adjacent sides . An exterior angle of a triangle is the angle at any vertex between any side of the triangle and the adjacent side produced ; as ACD . B ...
... angles of the triangle are the B angles CAB , ABC , and BCA , included between the adjacent sides . An exterior angle of a triangle is the angle at any vertex between any side of the triangle and the adjacent side produced ; as ACD . B ...
Page 28
... angle of one are equal respectively to the hypote- nuse and an adjacent angle of the other . Given , in rt . A ABC ... exterior angles . c and f , or d and e , are called alter- nate - interior angles . ( § 45 ) a / b A B c / d elf D g / h a ...
... angle of one are equal respectively to the hypote- nuse and an adjacent angle of the other . Given , in rt . A ABC ... exterior angles . c and f , or d and e , are called alter- nate - interior angles . ( § 45 ) a / b A B c / d elf D g / h a ...
Page 38
... exterior angle of a triangle is equal to the sum of the two opposite interior angles . 2. An exterior angle of a triangle is greater than either of the opposite interior angles . 86. Cor . II . If two triangles have two angles of one ...
... exterior angle of a triangle is equal to the sum of the two opposite interior angles . 2. An exterior angle of a triangle is greater than either of the opposite interior angles . 86. Cor . II . If two triangles have two angles of one ...
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Common terms and phrases
ABē AC and BC ACē ADē adjacent angles altitude angles are equal apothem approach the limit arc BC BCē bisector bisects centre cents chord circumference circumscribed common point construct the triangle Converse of Prop decagon diameter Draw line EFGH equal angles equal respectively equally distant equiangular equiangular polygon equivalent exterior angle Given line given point given straight line homologous sides hypotenuse intersecting isosceles triangle line CD line joining measured by arc meeting middle point non-parallel sides number of sides opposite sides parallel parallelogram perimeter perpendicular points of sides polygons AC produced Prove Proof quadrilateral radii radius ratio rectangle regular inscribed regular polygon rhombus right angles right triangle segments side BC sides are equal similar triangles subtended tangent THEOREM transversal trapezoid triangles are equal vertex
Popular passages
Page 220 - The perpendiculars from the vertices of a triangle to the opposite sides are the bisectors of the angles of the triangle formed by joining the feet of the perpendiculars.
Page 39 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 47 - ... the three sides of one are equal, respectively, to the three sides of the other. 2. Two right triangles are congruent if...
Page 69 - A chord is a straight line joining the extremities of an arc ; as AB.
Page 147 - If one leg of a right triangle is double the other, the perpendicular from the vertex of the right angle to the hypotenuse divides it into segments which are to each other as 1 to 4.
Page 188 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Page 138 - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Page 159 - DB as often as possible. As the lines AD and DB are incommensurable, there must be a remainder, B'B, less than one of the equal parts. Draw B'C
Page 47 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.