## The Essentials of Geometry (plane) |

### From inside the book

Results 1-5 of 65

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**sides**AB and**BC**on**sides**DE and EF , respec- tively , the angles are equal ...**BC**are not equal in length to**sides**DE and EF , respectively . 23. Two angles are said to be adjacent . when they have the same vertex , and a common**side**... Page 23

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**BC**, and CA , are called the**sides**of the triangle , and their points of intersection , A , B , and C , the vertices ...**side**of the triangle and the adjacent**side**produced ; as ACD . B 58. A triangle is called scalene when no two ... Page 24

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**BC**is the base , AD the altitude , and BAC the vertical angle . B D 61. Since a straight line is the shortest line between two points ( Ax . 4 ) , it follows that Any**side**of a triangle is less than the sum of the other two**sides**. PROP ... Page 24

... side DE , and side AC on side DF . Then since AB = DE and AC = DF , point B will fall on point E , and point C on point F. Whence ,

... side DE , and side AC on side DF . Then since AB = DE and AC = DF , point B will fall on point E , and point C on point F. Whence ,

**side BC**will coincide with side EF . [ But one str . line can be drawn between two points . ] ( Ax ... Page 24

... side AB shall coincide with its equal DE ; point A falling on point D , and point B on point E. Then since A = Z D , side AC will fall on side DF , and point C will fall somewhere on DF . And since B = ≤ E ,

... side AB shall coincide with its equal DE ; point A falling on point D , and point B on point E. Then since A = Z D , side AC will fall on side DF , and point C will fall somewhere on DF . And since B = ≤ E ,

**side BC**will fall on side ...### Other editions - View all

### 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.