## Plane Geometry |

### From inside the book

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Page 75

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**radii**are equal . All its diameters are equal , since a diameter is equal to two**radii**. 218. Postulate . A circumference can be described from any point as a centre , with any given radius . 219. A secant is a straight line of ... Page 76

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**radii**and the arc which they intercept . The angle included by the**radii**is called the angle of the sector ( Fig . 2 ) . 228. A quadrant is a sector equal to a quarter of the circle ( Fig . 2 ) . 229. An angle is called a central angle ... Page 77

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**radii**. For they will coincide , if their centres are made to coincide . CONVERSELY : Two equal circles have equal**radii**. 234. Two circles are concentric , if they have the same centre . ARCS , CHORDS , AND TANGENTS . PROPOSITION I ... Page 80

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**radii**OA , OB , OF , O'A ' , O'B ' . The AAOB and A'O'B ' are equal . § 143 For OA = O'A ' , and OB = O'B ' , § 233 (**radii**of equal circles ) , and AOBLA'O'B ' , § 237 ( in equal equal arcs subtend equal central 4 ) . § 128 .. chord AB ... Page 81

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**radii**OA , OB , OF , O'A ' , O'B ' . The AOAB and O'A'B ' are equal . For OA O'A ' , and OB O'B ' , = = = and chord AB = chord A'B ' . .. LAOB = L A'O'B ' . .. arc AB arc A'B ' , ( in equal equal central △ intercept equal arcs ) . 2 ...### Other editions - View all

### Common terms and phrases

ABē ABCD ACē adjacent angles altitude apothem base bisector bisects centre chord circumscribed circle coincide construct a square decagon diagonals diameter divided draw equiangular equidistant equilateral triangle exterior angle feet Find the area Find the locus given angle given circle given length given line given point given square given straight line given triangle greater Hence homologous sides hypotenuse inches inscribed circle intersecting isosceles trapezoid isosceles triangle limit line drawn mean proportional median middle point number of sides obtuse parallel parallelogram perimeter perpendicular PROBLEM Proof prove Q. E. D. PROPOSITION Q. E. F. Ex quadrilateral quantities radii rectangle regular polygon rhombus right angle right triangle secant segments similar polygons square equivalent straight angle tangent THEOREM third side trapezoid triangle ABC triangle is equal vertex vertices

### Popular passages

Page 94 - Any two sides of a triangle are together greater than the third side.

Page 42 - If two triangles have two sides of the 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 191 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.

Page 156 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.

Page 75 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.

Page 71 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.

Page 38 - Two triangles are equal if the three sides of the one are equal respectively to the three sides of the other. In the triangles ABC and A'B'C', let AB = A'B', AC = A'C', BC=B'C'. To prove A ABC= A A'B'C'. Proof. Place A A'B'C' in the position AB'C, having its greatest side A'C' in coincidence with its equal AC, and its vertex at B', opposite B ; and draw BB'.

Page 55 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.

Page 50 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.

Page 33 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles, and therefore greater than either of them.