A Text-book of GeometryGinn, 1888 - 386 σελίδες |
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Σελίδα 57
... diagonal of a quadrilateral is a straight line joining two opposite vertices . PROPOSITION XXXVI . THEOREM . 178. The diagonal of a parallelogram divides the figure into two equal triangles . B E Let ABCE be a parallelogram and AC its ...
... diagonal of a quadrilateral is a straight line joining two opposite vertices . PROPOSITION XXXVI . THEOREM . 178. The diagonal of a parallelogram divides the figure into two equal triangles . B E Let ABCE be a parallelogram and AC its ...
Σελίδα 58
... diagonal of a □ divides the figure into two equal △ ) . = .. BC AE , and AB CE , = § 178 Also , ( being homologous sides of equal △ ) . LB ( having their sides || and extending in opposite directions from LE , and Z BAE = BCE ...
... diagonal of a □ divides the figure into two equal △ ) . = .. BC AE , and AB CE , = § 178 Also , ( being homologous sides of equal △ ) . LB ( having their sides || and extending in opposite directions from LE , and Z BAE = BCE ...
Σελίδα 60
... , if the alt . - int . & are equal , the lines are parallel ) . .. the figure ABCE is a □ , ( having its opposite sides parallel ) . $ 168 Q. ED . PROPOSITION XL . THEOREM . 184. The diagonals of a 60 PLANE GEOMETRY . - BOOK I.
... , if the alt . - int . & are equal , the lines are parallel ) . .. the figure ABCE is a □ , ( having its opposite sides parallel ) . $ 168 Q. ED . PROPOSITION XL . THEOREM . 184. The diagonals of a 60 PLANE GEOMETRY . - BOOK I.
Σελίδα 61
... diagonals AC and BE cut each other at 0 . To prove = AO OC , and BO = OE . In the A AOE and BOC AE = BC , § 168 ... diagonals of a quadrilateral bisect each other , the figure is a parallelogram . Ex . 26. The diagonals of a rectangle ...
... diagonals AC and BE cut each other at 0 . To prove = AO OC , and BO = OE . In the A AOE and BOC AE = BC , § 168 ... diagonals of a quadrilateral bisect each other , the figure is a parallelogram . Ex . 26. The diagonals of a rectangle ...
Σελίδα 64
... diagonal DB . In the A ADB join E , the middle point of AD , to F , the middle point of DB . Then , by § 189 , EF is to AB and join Fto G , the middle point of BC . and DC . AB and FG , being II to = AB . In the △ DBC Then FG is to DC ...
... diagonal DB . In the A ADB join E , the middle point of AD , to F , the middle point of DB . Then , by § 189 , EF is to AB and join Fto G , the middle point of BC . and DC . AB and FG , being II to = AB . In the △ DBC Then FG is to DC ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AB² ABCD AC² acute angle altitude angles are equal apothem base bisector bisects called centre chord circumference circumscribed circumscribed circle coincide decagon diagonal diameter divide Draw equal angles equal respectively equiangular equiangular polygon equidistant equilateral triangle exterior angles feet figure Find the area given circle given line given point given straight line given triangle greater Hence homologous sides hypotenuse inches intersect isosceles trapezoid isosceles triangle legs length line joining measured by arc middle points number of sides parallel parallelogram perimeter perpendicular prove Proof Q. E. D. Ex Q. E. D. PROPOSITION quadrilateral radii ratio rectangle regular inscribed regular polygon rhombus right angle right triangle SCHOLIUM secant segments shortest side similar polygons straight angle subtended tangent THEOREM third side trapezoid triangle ABC triangle is equal vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 44 - 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 144 - 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'.
Σελίδα 130 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Σελίδα 128 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Σελίδα 211 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Σελίδα 157 - 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.
Σελίδα 152 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Σελίδα 187 - ... upon the sum of two straight lines is equivalent to the sum of the squares described on the two lines plus twice their rectangle. Note. By the "rectangle of two lines" is here meant the rectangle of which the two lines are the adjacent sides.
Σελίδα 136 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Σελίδα 15 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line. 3.