Plane and Solid GeometryAmerican Book Company, 1899 - 384 σελίδες |
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Αποτελέσματα 1 - 5 από τα 52.
Σελίδα 30
... points H and J. To prove the alternate interior an- gles , as AHJ and DJH , equal . G H B Proof . Through L , the middle point of HJ , draw GK CD . Then , § 72 , GK AB . Revolve the figure JLK about the point L and apply it to the ...
... points H and J. To prove the alternate interior an- gles , as AHJ and DJH , equal . G H B Proof . Through L , the middle point of HJ , draw GK CD . Then , § 72 , GK AB . Revolve the figure JLK about the point L 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 ABC and ABF , and ... § 100 , That is , Therefore , etc. Lr = Ls . AC AF , AB is common , < r = 2s ; AABC = AABF . ΔΑΒΟ = ΔΙΕΡ . Q.E.D. Prove by placing the triangle so that ( 1 ) DF will coincide with AC ...
... middle point , and , § 105 , In ABC and ABF , and ... § 100 , That is , Therefore , etc. Lr = Ls . AC AF , AB is common , < r = 2s ; AABC = AABF . ΔΑΒΟ = ΔΙΕΡ . Q.E.D. 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 cylinder Data diagonals diameter dihedral angles distance divided equal circles equidistant equilateral triangle equivalent exterior angle extremities FGHJK Find the locus frustum given line given point given straight line Hence homologous sides hypotenuse inscribed angle intersecting isosceles trapezoid isosceles triangle measured by arc middle point number of sides opposite sides parallel lines parallelogram parallelopiped pass perimeter perpendicular plane polyhedron prism produced Proof prove pyramid Q.E.D. Proposition quadrilateral radii radius ratio rect rectangle formed regular polygon respectively rhombus right angle right triangle secant segments sphere spherical triangle subtended surface tangent Theorem transversal trapezoid triangle ABC triangles are equal trihedral vertex vertical angle volume
Δημοφιλή αποσπάσματα
Σελίδα 67 - 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 47 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Σελίδα 64 - 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 33 - 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 219 - 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 217 - The. sum of the angles of any polygon is equal to twice as many right angles as the polygon has sides, less four right angles.
Σελίδα 136 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Σελίδα 90 - 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.
Σελίδα 374 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Σελίδα 176 - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.