The Elements of Plane and Solid Geometry: With Numerous ExercisesD.C. Heath & Company, 1890 - 393 Seiten |
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Seite 46
... diagonals . 122. A trapezium is a quadrilateral which has no two of its sides parallel . 123. A trapezoid is a quadrilateral which has two of its sides parallel . The parallel sides of a trapezoid are called the bases , and the ...
... diagonals . 122. A trapezium is a quadrilateral which has no two of its sides parallel . 123. A trapezoid is a quadrilateral which has two of its sides parallel . The parallel sides of a trapezoid are called the bases , and the ...
Seite 47
... diagonal AC . D = B. ZB . A B Because DC is to AB , ( Hyp . ) and AD is || to BC , ( Hyp . ) ... = and Hence the whole ( Ax . 9 ) Now in the J < DCA = < BAC , Į ( just proved ) < DCA BAC , < < ACB CAD , = being alt . - int . Ls ( 72 ) ...
... diagonal AC . D = B. ZB . A B Because DC is to AB , ( Hyp . ) and AD is || to BC , ( Hyp . ) ... = and Hence the whole ( Ax . 9 ) Now in the J < DCA = < BAC , Į ( just proved ) < DCA BAC , < < ACB CAD , = being alt . - int . Ls ( 72 ) ...
Seite 48
... diagonal AC . In the As ACD , ACB , because AD BC , AB = CD , ( Hyp . ) ( Hyp . ) and AC is common , .. A ACD = △ ACB . ( 108 ) and and ... ZACD / CAB , = / CAD - ACB , being homologous Ls of equal △ s ( 109 ) . ... AB is || to CD ...
... diagonal AC . In the As ACD , ACB , because AD BC , AB = CD , ( Hyp . ) ( Hyp . ) and AC is common , .. A ACD = △ ACB . ( 108 ) and and ... ZACD / CAB , = / CAD - ACB , being homologous Ls of equal △ s ( 109 ) . ... AB is || to CD ...
Seite 49
... diagonal AC . In the As ACD , ACB , because A B AB = : CD , ( Hyp . ) AC is common , ZACD = CAB , being alt . - int . ≤8 ( 72 ) , . ' . △ ACD = △ ACB , having two sides and ... diagonals of a parallelogram BOOK I. - QUADRILATERALS . 49.
... diagonal AC . In the As ACD , ACB , because A B AB = : CD , ( Hyp . ) AC is common , ZACD = CAB , being alt . - int . ≤8 ( 72 ) , . ' . △ ACD = △ ACB , having two sides and ... diagonals of a parallelogram BOOK I. - QUADRILATERALS . 49.
Seite 50
... diagonals of a quadrilateral bisect each other , the figure is a parallelogram . 3. If the diagonals of a parallelogram are equal , the fig- ure is a rectangle ; if they also intersect at right angles , it is a square . 4. The straight ...
... diagonals of a quadrilateral bisect each other , the figure is a parallelogram . 3. If the diagonals of a parallelogram are equal , the fig- ure is a rectangle ; if they also intersect at right angles , it is a square . 4. The straight ...
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Häufige Begriffe und Wortgruppen
ABCD adjacent angles altitude angles are equal base bisect bisector called centre chord circumference circumscribed coincide common cone of revolution Cons construct cylinder diagonals diameter diedral angle distance divided draw equally distant equivalent EXERCISES exterior angle faces feet Find the area Find the volume frustum given circle given line given point given straight line homologous homologous sides hypotenuse inches intersection isosceles triangle lateral area lateral edges Let ABC meet middle point number of sides parallel parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced Proposition Proposition 13 pyramid quadrilateral radii radius ratio rectangle rectangular parallelopiped regular inscribed regular polygon right angles segment similar slant height sphere spherical polygon spherical triangle square surface symmetrical tangent tetraedron Theorem triangle ABC triangular prism triedral vertex
Beliebte Passagen
Seite 74 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.
Seite 188 - 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.
Seite 45 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Seite 137 - Terms of the proportion. The first and fourth terms are called the Extremes, and the second and third the Means.
Seite 12 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.
Seite 206 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Seite 97 - BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference.
Seite 334 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Seite 12 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 253 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.