## Essentials of Geometry (plane). |

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### Common terms and phrases

ABCD acute adjacent altitude arc BC base bisector bisects called centre chord circle circumference circumscribed coincide common construct describe diagonals diameter difference divided Draw line drawn equal equally distant equilateral equivalent EXERCISES exterior angle extremities fall figure Find follows Geometry given Given line given point greater Hence hypotenuse included inscribed intersect isosceles triangle length less line joining manner mean measured meeting middle point one-half opposite sides parallel parallelogram passes perimeter perpendicular plane polygon PROBLEM produced Proof PROP proportional Prove quadrilateral radii radius ratio rectangle regular inscribed Required respectively right angles right triangle segment side BC similar square straight line surface tangent THEOREM third transversal trapezoid triangle ABC unit values vertex vertices

### 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.