## Plane and Solid Geometry |

### From inside the book

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**straight lines at their point of intersection , it is perpendicular to the plane of**the two lines . Data : Any two straight lines , as AB and CD , intersecting at E ; MN , the plane of these lines ; and HE , a perpendicular to AB and CD ...### Other editions - View all

### Common terms and phrases

ABCD adjacent angles altitude angle formed angles are equal angles compare apothem arc intercepted base bisector bisects called central angle chord circle whose center circumference circumscribed compare in length Construct a triangle cylinder Data diagonals diameter dihedral angles distance divided equal circles equidistant equilateral triangle equivalent exterior angle extremities FGHJK Find the locus frustum given line given point given straight line Hence homologous sides hypotenuse inscribed angle intersecting isosceles trapezoid isosceles triangle measured by arc middle point number of sides opposite sides parallel lines parallelogram parallelopiped pass perimeter perpendicular plane polyhedron prism produced Proof prove pyramid Q.E.D. Proposition quadrilateral radii radius ratio rect rectangle formed regular polygon respectively rhombus right angle right triangle secant segments sphere spherical triangle subtended surface tangent Theorem transversal trapezoid triangle ABC triangles are equal trihedral vertex vertical angle volume

### Popular passages

Page 67 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.

Page 47 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...

Page 64 - From 56 and 57 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other...

Page 33 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.

Page 219 - 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 217 - The. sum of the angles of any polygon is equal to twice as many right angles as the polygon has sides, less four right angles.

Page 136 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.

Page 90 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.

Page 374 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 176 - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.