## Plane and Solid Geometry |

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Page

Exercises in geometrical

lines or equal angles in the same color , or if this is impracticable , mark them by

equal viii SUGGESTIONS TO TEACHERS crossmarks ; denote parallel lines by

vii.

Exercises in geometrical

**drawing**( e . g . S $ 113 , 114 , 115 , etc . ) ...**Draw**equallines or equal angles in the same color , or if this is impracticable , mark them by

equal viii SUGGESTIONS TO TEACHERS crossmarks ; denote parallel lines by

vii.

Page

viii SUGGESTIONS TO TEACHERS crossmarks ; denote parallel lines by arrows ;

. g . yellow , etc . The following diagrams illustrate the method . The diagrams ...

viii SUGGESTIONS TO TEACHERS crossmarks ; denote parallel lines by arrows ;

**draw**a greater line in some color , e . g . green , a smaller line in another color , e. g . yellow , etc . The following diagrams illustrate the method . The diagrams ...

Page 16

Arthur Schultze, Frank Louis Sevenoak. Proof . Let E be the midpoint of BC .

= EF and BE = EC . ( Con . ) Z BEANZ FEC , ( vertical & ) . . : A ABE = A FCE , ( s .

a .

Arthur Schultze, Frank Louis Sevenoak. Proof . Let E be the midpoint of BC .

**Draw**AE and produce it its own length to F .**Draw**FC . - - - - A ABE and FCE , AE= EF and BE = EC . ( Con . ) Z BEANZ FEC , ( vertical & ) . . : A ABE = A FCE , ( s .

a .

Page 25

THEOREM 93 . The sum of the angles of a triangle is equal to a straight angle . D

- - - - - - - - - - E B Hyp . ABC is a triangle . To prove 2A + 2B + _ C = a st . Z . Proof

.

...

THEOREM 93 . The sum of the angles of a triangle is equal to a straight angle . D

- - - - - - - - - - E B Hyp . ABC is a triangle . To prove 2A + 2B + _ C = a st . Z . Proof

.

**Draw**line DE | | BC through A . ZB = _ DAB ) ZC = CAE / ( alt . int . & of II lines . )...

Page 38

BC . Q . E . F . [ The proof is left to the student . ] ( 111 ) Ex . 154 . Construct the

three altitudes of an acute triangle ; of an obtuse triangle . Ex . 155 . From a given

...

**Draw**AO intersecting BC in D . AD is a perpendicular from the point A to the lineBC . Q . E . F . [ The proof is left to the student . ] ( 111 ) Ex . 154 . Construct the

three altitudes of an acute triangle ; of an obtuse triangle . Ex . 155 . From a given

...

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### Common terms and phrases

ABCD altitude angle angles are equal base bisect bisector called chord circle circumference circumscribed coincide common cone construct contains corresponding cylinder diagonals diameter diedral angles difference distance divide draw drawn equal equidistant equivalent exterior angle faces figure Find formed four geometrical given circle given line given point greater Hence homologous hypotenuse inches included inscribed intersecting isosceles triangle length less limit line joining measured median meet midpoints opposite sides parallel parallel lines parallelogram passing perimeter perpendicular plane polyedron polygon prism PROBLEM Proof PROPOSITION prove prove Hyp pyramid quadrilateral radii radius ratio rectangle regular polygon respectively right angles right triangle School segments sides similar sphere spherical triangle square straight line surface tangent THEOREM third transform triangle triangle are equal vertex vertices

### Popular passages

Page 148 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 150 - If, from a point without a circle, a tangent and a secant be drawn, the tangent is the mean proportional between the secant and its external segment.

Page 180 - Two triangles having 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.

Page 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle 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 337 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...

Page 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes ; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.

Page 312 - The lateral areas, or the total areas, of similar cylinders of revolution are to each other as the squares of their altitudes, or as the squares of their radii ; and their volumes are to each other as the cubes of their altitudes, or as the cubes of their radii. Let S, S' denote the lateral areas, T, T...

Page 149 - If, from a point without a circle, two secants are drawn, the product of one secant and its external segment is equal to the product of the other and its external segment.

Page 328 - Every section of a sphere made by a plane is a circle.

Page 257 - If two intersecting planes are each perpendicular to a third plane, their intersection is perpendicular to that plane.