## Plane and Solid Geometry |

### From inside the book

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**Intersecting**Planes 281 Lines and Planes , Parallel 283 Lines and Planes , Perpendicular 288 Projections . Diedral Angles Polyedral Angles 293 295 .302 Loci . General Exercises Definitions . CHAPTER VII . POLYEDRONS 4 CONTENTS. Page 11

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**intersect**each other is a point . The ends of a line are points . The place where a line is separated into parts is a point . N H D K G E B A -F The lines HK and NK meet at the point K. The lines DF and GE**intersect**at the point O ... Page 15

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**intersect**each other at two points D and E. Draw the line ' DE**intersecting**AB at 0 . The line AB is A -B O bisected at the point 0 . With the aid of compasses , show that AO is equal to OB . Draw lines one , two , three , and four ... Page 23

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**intersecting**the first arc at K. Draw KH and KE . ΔΗΚΕ is constructed with its sides equal to 5 cm . , 4 cm . , and 3 cm . , respectively . 25. To construct a triangle when the three sides are given . Construct a triangle with its sides ... Page 27

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**intersects**another straight line , the vertical angles are equal . Proof of this statement may be found in § 56 . EXERCISES When A and ZB of a triangle ABC have the following values , find the value of ZC : 1. ZA = 60 ° , ≤B = 70 ...### 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.