## Plane Geometry |

### From inside the book

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**rhombus**is a rhomboid which has its sides equal . Square . Rectangle .**Rhombus**. Rhomboid . 171. The side upon which a parallelogram stands , and the opposite side , are called its lower and upper bases . 172. Two parallel sides of a ... Page 72

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**rhombus**are perpendicular to each other , and bisect the angles of the**rhombus**. Ex . 72. The diagonals of a square are perpendicular to each other , and bisect the angles of the square . Ex . 73. Lines from two opposite vertices of a ... Page 73

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**rhombus**, taken in order , enclose a rectangle . ( Proof similar to that of Ex . 74. ) Ex . 76. The lines joining the middle points of the sides of a rectangle ( Lot a square ) , taken in order , enclose a**rhombus**. Ex . 77. The lines ... Page 111

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**rhombus**. H G H B E E B M N D F Ex . 133. The bisectors of the angles included by the opposite sides ( produced ) of an inscribed quadrilaterai intersect at right angles . Arc AF arc BM = arc DF and arc AH - - arc CM arc DN = arc BH arc ... Page 132

... and the angle between the diagonals . To construct a

... and the angle between the diagonals . To construct a

**rhombus**, having given : Ex . 212. The two diagonals . Ex . 213. One side and the radius of the inscribed circle . Ex . 214. One angle and the radius of the 132 BOOK II . PLANE GEOMETRY .### 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.