Plane and Solid GeometryAmerican Book Company, 1899 - 384 σελίδες |
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Αποτελέσματα 1 - 5 από τα 51.
Σελίδα 30
... points H and J. To prove the alternate interior an- gles , as AHJ and DJH , equal . E G H B Proof . Through L , the middle point of HJ , draw GK 1 CD . Then , § 72 , GK AB . Revolve the figure JLK about the point I and apply it to the ...
... points H and J. To prove the alternate interior an- gles , as AHJ and DJH , equal . E G H B Proof . Through L , the middle point of HJ , draw GK 1 CD . Then , § 72 , GK AB . Revolve the figure JLK about the point I and apply it to the ...
Σελίδα 42
... middle point ; select any point in the perpendicular and from that point draw straight lines to the extremities of the given line . How do these lines compare in length ? How do the angles made by these lines with the perpendicular ...
... middle point ; select any point in the perpendicular and from that point draw straight lines to the extremities of the given line . How do these lines compare in length ? How do the angles made by these lines with the perpendicular ...
Σελίδα 43
... middle point of that line . 105. Cor . II . If a perpendicular is erected at the middle point of a straight line , the lines joining the extremities of this line with any point in the perpendicular make equal angles with the line and ...
... middle point of that line . 105. Cor . II . If a perpendicular is erected at the middle point of a straight line , the lines joining the extremities of this line with any point in the perpendicular make equal angles with the line and ...
Σελίδα 44
... middle point , and , § 105 , In A ABC and ABF , and .. § 100 , That is , Therefore , etc. < r = Ls . AC = AF , AB is common , Zr = 2s ; ΔΑΒΟ = ΔΑΒΡ . △ ABC A DEF . = Prove by placing the triangle so that ( 1 ) DF will coincide with AC ...
... middle point , and , § 105 , In A ABC and ABF , and .. § 100 , That is , Therefore , etc. < r = Ls . AC = AF , AB is common , Zr = 2s ; ΔΑΒΟ = ΔΑΒΡ . △ ABC A DEF . = Prove by placing the triangle so that ( 1 ) DF will coincide with AC ...
Σελίδα 45
... middle point of the side BC of the triangle ABC , and BE and CF are perpendiculars from B and C to AD , or AD produced , how do BE and CF compare in length ? Proposition XXII 110. 1. Cut out a paper triangle ABC . Cut off the corners ...
... middle point of the side BC of the triangle ABC , and BE and CF are perpendiculars from B and C to AD , or AD produced , how do BE and CF compare in length ? Proposition XXII 110. 1. Cut out a paper triangle ABC . Cut off the corners ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles altitude angle formed angles are equal angles compare apothem arc intercepted base bisector bisects called central angle chord circle whose center circumference circumscribed compare in length Construct a triangle Data diagonals diameter dihedral angles distance divide equal circles equidistant equilateral triangle equivalent exterior extremities Find the locus frustum given line given point given straight line Hence homologous homologous sides hypotenuse inscribed angle interior angles intersecting isosceles trapezoid isosceles triangle line drawn measured by arc middle point number of sides opposite sides parallel lines parallelogram parallelopiped pass perimeter perpendicular plane prism produced Proof proportion prove pyramid Q.E.D. Proposition quadrilateral radii radius ratio rect rectangle formed regular polygon respectively rhombus right angles right triangle secant segment similar sphere spherical triangle subtended surface tangent Theorem transversal trapezoid triangle ABC triangles are equal trihedral vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 103 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 147 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Σελίδα 65 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Σελίδα 45 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Σελίδα 62 - From 56 and 57 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other...
Σελίδα 59 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.
Σελίδα 81 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Σελίδα 45 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 31 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
Σελίδα 88 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.