Schultze and Sevenoak's Plane and Solid Geometry |
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Page 5
... sides lie in the same straight line but extend in opposite directions , as ABC . C B A 26. DEF . A right angle is an angle equal to one half of a straight angle . Thus , if OC bisects the straight angle AOB , angle 3 and angle 4 are ...
... sides lie in the same straight line but extend in opposite directions , as ABC . C B A 26. DEF . A right angle is an angle equal to one half of a straight angle . Thus , if OC bisects the straight angle AOB , angle 3 and angle 4 are ...
Page 13
... sides of a triangle are equal , the angles opposite are equal , " is a theorem . The conditional part of the statement is called the hypothesis , the assertion that is to be proved is called the conclusion . Thus in the above example ...
... sides of a triangle are equal , the angles opposite are equal , " is a theorem . The conditional part of the statement is called the hypothesis , the assertion that is to be proved is called the conclusion . Thus in the above example ...
Page 15
... opposite sides are equal . ( c ) Two triangles are congruent if the 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 ...
... opposite sides are equal . ( c ) Two triangles are congruent if the 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 ...
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 ...
Page 32
... side longer than BC . Place A ABC so that BC shall coincide with B'C ' and 4 and A ' lie on opposite sides of B'C ' . Draw AA ' . A AB'A ' is isosceles . ../1=Z 2 . A AC'A ' is isosceles . ..Z3 = 24 . ..21 + 23 = 22 + 24 . LA = LA ...
... side longer than BC . Place A ABC so that BC shall coincide with B'C ' and 4 and A ' lie on opposite sides of B'C ' . Draw AA ' . A AB'A ' is isosceles . ../1=Z 2 . A AC'A ' is isosceles . ..Z3 = 24 . ..21 + 23 = 22 + 24 . LA = LA ...
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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.