## The Essentials of Geometry (plane) |

### From inside the book

Results 1-5 of 90

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**Prove**, and**Proof**, printed in heavy - faced type . A similar system is followed in the Constructions , by the use of the words Given , Re- quired , Construction , and**Proof**. A minor improvement is the omission of the definite article ... Page 10

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**prove**the sum of angles AOB , BOC , COD , and DOA equal to four right angles . Produce 40 to E. Then , the sum of ...**proved**. 3. The**proof**. In the remaining propositions of the work , we shall mark clearly the three divisions of ... Page 11

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**Prove**that AC and BC lie in the same str . line .**Proof**. If AC and BC do not lie in the same str . line , let CE be in the same str . line with AC . Then since ACE is a str . line , ECD is the supplement of Z ACD . [ If two adj ... Page 12

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**Prove**ZAOC = Z BOD .**Proof**. Since AOC and , AOD have their ext . sides in str . line CD , ZAOC is the supplement of AOD . [ If two adj . have their ext . sides in the same str . line , they are supplementary . ] ( § 33 ) For the same ... Page 13

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**Prove**AE = BE .**Proof**. Superpose figure BDE upon figure ADE by fold- ing it over about line DE as an axis . Now ZBDE : = ZADE . [ All rt . are equal . ] Then , line BD will fall upon line AD . ( § 26 ) But by hyp . , BD = AD . Whence ...### 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.