## Plane and Solid Geometry |

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**slant**is 1 ft . in a vertical rise of 12 ft . 16. In a right prism whose volume is 54 , the lateral area is four ...**height**of the segment occupied by the steam is 18 in . ( Use ( 2 ) of $ 509 ) . 21. A cylindrical tank of diameter ... Page 344

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**slant height**. In the figure , OV is the altitude , BV a lateral edge , and NV the**slant height**. A E D N В C REGULAR PYRAMID 703. Circular Cones . A cone whose base is a circle is called a circular cone . The line joining the vertex of ... Page 345

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**slant height**. 705. Prove the following facts concerning cones and pyramids : ( 1 ) The lateral faces of a regular pyramid are congruent isos- celes triangles . ( 2 ) The lateral edges of a regular pyramid are equal . ( 3 ) The elements ... Page 349

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**slant height**. S = ps . Given the regular pyramid V - ABCDE . To prove Sps , where S denotes lateral area , s**slant height**, and p perimeter of base . Proof . The lateral faces are congruent tri- angles . The area of each face triangle ... Page 350

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**slant height**of the cone , and N A 8 B 2 Tr whose arc is equal to the circumference of the base of the cone . Then , by 508 , the lateral area of a right circular cone is equal to half the product of the**slant height**and the ...### Contents

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### Common terms and phrases

AABC ABCD acute angle altitude angles are equal angles equal base bisects chord circumference circumscribed congruent diagonals diameter diedral angles distance divided Draw drawn equal respectively equilateral triangle equivalent EXERCISES face angles figure Find the area Find the length Find the number Find the radius Find the volume formula frustum given circle given line given point hypotenuse inch interior angles intersecting isosceles trapezoid isosceles triangle lateral area lateral edges locus median middle point number of sides parallel lines parallelepiped parallelogram perimeter plane geometry plane Q polyedral angle polyedron prism prismatoid Proof prove pyramid quadrilateral radii ratio rectangle regular polygon rhombus right angle right circular cone right triangle segment semicircle Show similar slant height sphere spherical angles spherical polygon spherical triangle straight line surface tangent tetraedron Theorem trapezoid triangle ABC triedral vertex angle vertices

### Popular passages

Page 169 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.

Page 75 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 19 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.

Page 155 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.

Page 89 - Two triangles are congruent if two sides and the included angle of one are equal respectively to two sides and the included angle of the other.

Page 164 - Two triangles which have an angle of one equal to the supplement of an angle of the other are to each other as the products of the sides including the supplementary angles.

Page 155 - ... any two parallelograms are to each other as the products of their bases by their altitudes. PROPOSITION V. THEOREM. 403. The area of a triangle is equal to half the product of its base by its altitude.

Page 248 - ... as the squares of their radii, or as the squares of their...

Page 296 - Axiom. Through a given point only one straight line can be drawn parallel to a given straight line.

Page 39 - In an isosceles triangle the angles opposite the equal sides are equal.