Plane and Solid GeometryMacmillan, 1902 - 370 σελίδες |
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Αποτελέσματα 6 - 10 από τα 56.
Σελίδα 8
... greater than any of its parts . 10. A straight line is the shortest distance b points . ( For Axiom 11 , see page 17 on parallel lines . ) POSTULATES 1. A straight line can be drawn between any tw 2. A straight line can be produced ...
... greater than any of its parts . 10. A straight line is the shortest distance b points . ( For Axiom 11 , see page 17 on parallel lines . ) POSTULATES 1. A straight line can be drawn between any tw 2. A straight line can be produced ...
Σελίδα 15
... such triang Ex . 42. If in triangle ABC , AB = BC , then △ A = △ C. PROPOSITION IV . THEOREM 75. An exterior angle of a triangle is greater th either remote interior angle . Proof . Let E be the midpoint of BC . TRIANGLES.
... such triang Ex . 42. If in triangle ABC , AB = BC , then △ A = △ C. PROPOSITION IV . THEOREM 75. An exterior angle of a triangle is greater th either remote interior angle . Proof . Let E be the midpoint of BC . TRIANGLES.
Σελίδα 35
... From A and B as centers , with equal radii greater than AB , describe arcs intersecting at C and E. Join CE . Then the line CE bisects AB at D. Q.E.F. Proof . Two points equidistant from the ends of a CONSTRUCTIONS 35.
... From A and B as centers , with equal radii greater than AB , describe arcs intersecting at C and E. Join CE . Then the line CE bisects AB at D. Q.E.F. Proof . Two points equidistant from the ends of a CONSTRUCTIONS 35.
Σελίδα 36
... greater than one - half the distance from B to C , describe two arcs intersect- ing at D. Join AD . AD bisects / CAB . Q.E.F. HINT . - What is the usual means of proving the equality of angles ? Ex . 141. Divide an angle into four equal ...
... greater than one - half the distance from B to C , describe two arcs intersect- ing at D. Join AD . AD bisects / CAB . Q.E.F. HINT . - What is the usual means of proving the equality of angles ? Ex . 141. Divide an angle into four equal ...
Σελίδα 37
... greater than OC , describe two arcs intersecting at E. Join OE . OE is the perpendicular to the line AB at O. [ The proof is left to the student . ] Q.E.F. Ex . 145. Construct the complement of a given angle . What kind of an angle must ...
... greater than OC , describe two arcs intersecting at E. Join OE . OE is the perpendicular to the line AB at O. [ The proof is left to the student . ] Q.E.F. Ex . 145. Construct the complement of a given angle . What kind of an angle must ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal bisect bisector chord circumference circumscribed cone construct a triangle cylinder diagonals diagram for Prop diameter diedral angles divide draw drawn equiangular 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 homologous sides hypotenuse inches inscribed intersecting isosceles triangle joining the midpoints lateral area lateral edges line joining mean proportional median opposite sides parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyedral angle polyedron prism PROPOSITION prove Proof quadrilateral radii ratio rectangle regular polygon respectively equal rhombus right angles right triangle SCHOLIUM segment similar triangles sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal triedral vertex
Δημοφιλή αποσπάσματα
Σελίδα 45 - 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.
Σελίδα 119 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 180 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 31 - The median to the base of an isosceles triangle is perpendicular to the base.
Σελίδα 305 - A cylinder is a solid bounded by a cylindrical surface and two parallel planes; the bases of a cylinder are the parallel planes; and the lateral surface is the cylindrical surface.
Σελίδα 337 - 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...
Σελίδα 250 - A straight line perpendicular to one of two parallel planes is perpendicular to the other also.
Σελίδα 297 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Σελίδα 105 - I. When the given point, A, is in the circumference. HINT. — What is the angle formed by a radius and a tangent at its extremity ? II. When the given point, A, is without the circle. \ Construction. Join A, and 0 the center of the given circle. On OA as a diameter, construct a circumference, intersecting the given circumference in B and C.
Σελίδα 276 - An oblique prism is equivalent to a right prism whose base is a right section of the oblique prism, and whose altitude is equal to a lateral edge of the oblique prism. Hyp. GM is a right section of oblique prism AD', and OM ' a right prism whose altitude is equal to a lateral edge of AD'. To prove AD' =s= GM'. Proof. The lateral edges of GM