Plane and Solid GeometryAmerican Book Company, 1899 - 384 σελίδες |
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Σελίδα 45
... Homologous parts . Ex . 52. Draw two parallel lines intersecting two parallel lines , and draw a line joining two opposite points of intersection . How do the triangles thus formed compare ? Ex . 53. Perpendiculars are drawn from the ...
... Homologous parts . Ex . 52. Draw two parallel lines intersecting two parallel lines , and draw a line joining two opposite points of intersection . How do the triangles thus formed compare ? Ex . 53. Perpendiculars are drawn from the ...
Σελίδα 74
... homologous sides of equal triangles . e . If they are sides of a triangle opposite equal angles . f . If they are sides of an equiangular triangle . § 36 § 91 § 103 § 108 § 118 § 119 § 132 § 134 § 139 k . If they are the sides of a ...
... homologous sides of equal triangles . e . If they are sides of a triangle opposite equal angles . f . If they are sides of an equiangular triangle . § 36 § 91 § 103 § 108 § 118 § 119 § 132 § 134 § 139 k . If they are the sides of a ...
Σελίδα 76
... homologous angles of equal triangles . § 83 $ 98 7. If they are formed adjacent to a straight line by lines joining the ex- tremities of that line with any point in its perpendicular bisector . § 105 § 105 § 108 § 113 § 116 r . If they ...
... homologous angles of equal triangles . § 83 $ 98 7. If they are formed adjacent to a straight line by lines joining the ex- tremities of that line with any point in its perpendicular bisector . § 105 § 105 § 108 § 113 § 116 r . If they ...
Σελίδα 78
... homologous angles in the two triangles are equal ? 9. What other homologous elements of the two triangles must also be equal before the triangles can be proved to be equal ? 10. By careful examination of the given figure discover ...
... homologous angles in the two triangles are equal ? 9. What other homologous elements of the two triangles must also be equal before the triangles can be proved to be equal ? 10. By careful examination of the given figure discover ...
Σελίδα 82
... homologous diagonals . Ex . 175. If two quadrilaterals have three angles and the two included sides of one equal , each to each , to three angles and the two included sides of the other , the quadrilaterals are equal . Ex . 176. The ...
... homologous diagonals . Ex . 175. If two quadrilaterals have three angles and the two included sides of one equal , each to each , to three angles and the two included sides of the other , the quadrilaterals are equal . Ex . 176. The ...
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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.