## Plane and Solid Geometry |

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### Common terms and phrases

ABCD adjoining altitude angle approaches assumed base bisector bisects Book called chord circle circular circumscribed coincide common Compare Conclusion cone congruent Construct cylinder Determine diagonals diameter diedral angles distance divided Draw drawn edges equal equidistant equilateral extended faces figure Find frustum geometry given given point greater Hence homologous hypotenuse Hypothesis inscribed intersect isosceles triangle joining lateral area length less limit locus means measure meet mid-point Note opposite parallel parallelogram pass perimeter perpendicular placed plane polygon prism Proof proportional PROPOSITION Prove pyramid radii radius ratio Recall rectangle regular represent respectively right angle segment sides similar sphere spherical square straight line studied Suggestion Supplementary Exercises surface tangent THEOREM third trapezoid triangle unit vertex vertices volume

### Popular passages

Page 162 - The sum of the squares of the two legs of a right triangle is equal to the square of the hypotenuse.

Page 203 - The areas of two similar triangles are to each other as the squares of any two homologous sides.

Page 166 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.

Page 82 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...

Page 101 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.

Page 205 - 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 162 - The square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides.

Page 293 - An equiangular polygon inscribed in a circle is regular if the number of its sides is odd. PROPOSITION VIII. THEOREM 405. Regular polygons of the same number of sides are similar. E Hyp. ABCDE and A'B'C'D'E' are regular polygons of n sides.

Page 128 - What is the locus of the vertex of the right angle of a right triangle which has a given hypotenuse ? 3.

Page 200 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.