## The Essentials of Geometry (plane) |

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### Common terms and phrases

AB² AC and BC AC² adjacent angles altitude angles are equal apothem approach the limit arc BC base and altitude BC² bisector bisects CD² centre chord circumference circumscribed construct the triangle Converse of Prop decagon diagonals diameter Draw line EFGH equal angles equal respectively equally distant equiangular polygon equilateral triangle equivalent exterior angle figure Given line given point given square homologous sides hypotenuse isosceles triangle line CD line joining measured by arc 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 secant segment side BC similar triangles subtended tangent THEOREM transversal trapezoid triangle is equal vertex ZAOB

### Popular passages

Page 73 - A chord is a straight line joining the extremities of an arc ; as AB.

Page 124 - In any proportion the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.

Page 122 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.

Page 151 - 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 224 - 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 40 - 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 38 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.

Page 192 - 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 193 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.

Page 142 - In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.