## Plane and Solid Geometry |

### From inside the book

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**bisectors**of vertical angles form one straight line . ( Converse of Ex . 19. ) 21 The**bisectors**of supplementary adjacent angles are perpendicular to each other . [ < a = Z a ' , and ≤ b = Zb ' by hyp . To prove a + ≤ b = a rt . Z ... Page 29

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**bisectors**of the corresponding angles are parallel . [ § 126. ] 3 The**bisectors**of the interior angles on the same side of the transversal are perpendicular to each other . [ Ex . 21 , § 124. ] 34 Perpendiculars to two parallels are ... Page 32

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**bisector**of an angle of a triangle is a straight line bisecting an angle and terminated by the opposite side . Every triangle has three angle -**bisectors**. 152 Classification of triangles . Triangle . Right . ( Acute . ( Isosceles ... Page 43

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**bisector**of the vertical angle of an isosceles triangle bisects the base at right angles . [ § 162. ] 67 If the ...**bisectors**of the base angles is isosceles . [ Ax . 9 , § 176. ] 76 In the triangle ABC , B = 2Z C. BD bisects B and ... Page 47

... an equilateral triangle is greater than the half of one side . 88 How many degrees are included between the

... an equilateral triangle is greater than the half of one side . 88 How many degrees are included between the

**bisectors**of two angles of an equilateral triangle ? PROPOSITION XXV . THEOREM 186 Every point in the perpendicular TRIANGLES 47.### Contents

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### Common terms and phrases

ABCD altitude angles are equal arc BC assigned quantity base bisectors bisects chord circumference circumscribed circle CONCLUSION cone construct COROLLARY cylinder diagonals diameter diedral angles divided equiangular equiangular polygon equidistant equilateral triangle exterior angle Find the area Find the locus Find the ratio frustum given circle given line given point homologous sides hypotenuse HYPOTHESIS inches inscribed intersecting isosceles trapezoid isosceles triangle lateral area legs line of centers mean proportional median mid-points number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron prism PROOF Draw Prove pyramid Q. E. D. EXERCISES Q. E. D. PROPOSITION quadrilateral radii radius rectangle regular polygon rhombus right angles right triangle SCHOLIUM secant segments similar triangles slant height SOLUTION sphere spherical polygon spherical triangle straight line surface tangent THEOREM trapezoid triangle ABC triedral vertex volume

### Popular passages

Page 168 - In any triangle, the square of the 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 upon that side.

Page 41 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 38 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 35 - Any side of a triangle is less than the sum of the other two sides...

Page 242 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.

Page 174 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.

Page 172 - If from a point without a circle a tangent and a secant are drawn, the tangent is the mean proportional between the whole secant and its external segment.

Page 171 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 192 - The areas of two rectangles having equal altitudes are to each other as their bases.

Page 65 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...