## Solid Geometry |

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### Common terms and phrases

Allowing altitude axis base bottom called circle circular cylinder circumscribed coincide common Conclusion congruent construction contain Corollary cube cubic cylinder determine diagonal diameter diedral angle distance divided Draw drawn element equal equidistant EXERCISES face angles figure Find Find the lateral Find the volume foot frustum geometry given plane given point Hence hexagonal Hypothesis inscribed intersect lateral area lateral edges lateral faces length line-segment measure meet opposite parallel parallel planes parallelopiped passed perpendicular placed plane MN pole polyedral angle polyedron polygon prism projection proof proof in full proof is left Prove pyramid radius rectangular regular pyramid respectively right circular cone Show sides similar slant height solid sphere square straight line student SUGGESTION surface Theorem third total area traced triangle triedral vertex vertices volume wide 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.