## Solid Geometry |

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### Common terms and phrases

ABCD altitude angles are equal axis bisects circle circumscribed Conclusion congruent conical surface Corollary cube cubic foot determine a plane diagonal diedral angle Draw drawn equidistant EXERCISES face angles figure Find the lateral Find the volume frustum geometry given plane given point hexagonal Hypothesis inscribed intersecting planes lateral area lateral edges lateral faces line perpendicular line-segment parallel planes parallelogram perimeter perpendicular plane angle plane geometry plane MN plane parallel plane PQ pole polyedral angle prismatoid proof in full proof is left Prove radii radius rectangular parallelopiped regular polyedrons regular polygon regular pyramid right circular cone right prism right section sides slant height spherical angle spherical excess spherical polygon spherical triangle square straight line student SUGGESTION surface symmetrical tangent tetraedron Theorem total area traced triangular prism triangular pyramid triedral truncated vertex vertices Write the proof

### Popular passages

Page 434 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.

Page 402 - A Sphere is a solid bounded by a curved surface, all points of which are equally distant from a point within, called the Centre.

Page 443 - If the first of three things is greater than the second, and the second greater than the third, then the first is greater than the third.

Page 446 - 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. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove = — • A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 284 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.

Page 445 - ... they have an angle of one equal to an angle of the other and the including sides are proportional; (c) their sides are respectively proportional.

Page 444 - Two right triangles are equal if the hypotenuse and an acute angle of the one are equal respectively to the hypotenuse and an acute angle of the other.

Page 445 - In any proportion, the product of the extremes equals the product of the means.

Page 378 - The lateral area of a frustum of a right circular cone is equal to one half the product of its slant height and the sum of the circumferences of its bases.

Page 444 - If two sides and the included angle of one triangle are equal respectively to two sides and the included angle of another triangle, then the triangles are congruent.