Schultze and Sevenoak's Plane and Solid Geometry |
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Page 15
... sides of the one are respectively equal to the sides of the other . ( d ) Vertical angles are equal . Ex . 61. If in the annexed diagram 21 = 22 , and ≤2 = 23 , for what reason * does < 1 equal < 3 ? Ex . 62. If AB = DF , and CB DE ...
... sides of the one are respectively equal to the sides of the other . ( d ) Vertical angles are equal . Ex . 61. If in the annexed diagram 21 = 22 , and ≤2 = 23 , for what reason * does < 1 equal < 3 ? Ex . 62. If AB = DF , and CB DE ...
Page 17
... sides in a straight line , they are supplementary . ( Ax . 10. ) A B ( Ax . 3. ) 51. If two adjacent angles are supplementary , their exterior sides are in the same straight line . Their exterior sides form a straight angle ( 36 ) 17 ...
... sides in a straight line , they are supplementary . ( Ax . 10. ) A B ( Ax . 3. ) 51. If two adjacent angles are supplementary , their exterior sides are in the same straight line . Their exterior sides form a straight angle ( 36 ) 17 ...
Page 20
... sides . The lines are called the sides . The angles included by the ad- jacent sides are the angles of the polygon , and their vertices are the vertices of the polygon . An ex- terior angle is formed by a side and the prolongation of an ...
... sides . The lines are called the sides . The angles included by the ad- jacent sides are the angles of the polygon , and their vertices are the vertices of the polygon . An ex- terior angle is formed by a side and the prolongation of an ...
Page 21
... sides . TRIANGLES - PART I 57. A triangle is a polygon of three sides . 58. Triangles classified as to sides . A scalene triangle is a triangle no two sides of which are equal . An isosceles triangle is a triangle two sides of which are ...
... sides . TRIANGLES - PART I 57. A triangle is a polygon of three sides . 58. Triangles classified as to sides . A scalene triangle is a triangle no two sides of which are equal . An isosceles triangle is a triangle two sides of which are ...
Page 22
... side opposite the right angle . The sides including the right angle are sometimes called the arms of the right triangle . 63. DEF . An altitude of a triangle is the perpendicular from any vertex to the opposite side ( produced if ...
... side opposite the right angle . The sides including the right angle are sometimes called the arms of the right triangle . 63. DEF . An altitude of a triangle is the perpendicular from any vertex to the opposite side ( produced if ...
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Common terms and phrases
altitude angle equal angle formed angles are equal annexed diagram bisect bisector chord circumference circumscribed congruent cylinder diagonals diagram for Prop diameter dihedral angles divide draw drawn equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inscribed intersecting isosceles triangle lateral area lateral edge line joining locus median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism PROPOSITION prove Proof pyramid Q. E. D. Ex quadrilateral radii ratio rectangle reflex angle regular polygon respectively equal rhombus right angles right triangle segments sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal trihedral vertex angle vertices
Popular passages
Page 222 - Two triangles having 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.
Page 208 - The area of a rectangle is equal to the product of its base and altitude.
Page 183 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 160 - A line parallel to one side of a triangle divides the other two sides proportionally.
Page 82 - 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 70 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle 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 188 - Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
Page 409 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 333 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 193 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.