Modern geometry [ed.] with an appendix by W.B. Jack1876 |
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Página 16
... angles , DEB , AEC , on opposite sides of the common vertex , E ; such that the sides of one are the continuation of the sides of the other . Two E D A C B FIG . 33 . such angles are called vertically - opposite angles . Vertically - ...
... angles , DEB , AEC , on opposite sides of the common vertex , E ; such that the sides of one are the continuation of the sides of the other . Two E D A C B FIG . 33 . such angles are called vertically - opposite angles . Vertically - ...
Página 22
... opposite angles are in the same straight line . 4. From a given point on a straight line , two straight lines , and only two , can be drawn , making with it a given angle . 5. The sum of all the angles formed by a number of straight ...
... opposite angles are in the same straight line . 4. From a given point on a straight line , two straight lines , and only two , can be drawn , making with it a given angle . 5. The sum of all the angles formed by a number of straight ...
Página 38
... angles opposite to them are equal . " THEOREM ІХ . Hypothesis .- " When two angles of a triangle are equal , " Conclusion- " The sides opposite to them are equal . " The hypothesis of Theorem VIII . is the conclusion of Theorem IX ...
... angles opposite to them are equal . " THEOREM ІХ . Hypothesis .- " When two angles of a triangle are equal , " Conclusion- " The sides opposite to them are equal . " The hypothesis of Theorem VIII . is the conclusion of Theorem IX ...
Página 42
... opposite side of B C. A D Also suppose CD to make with BC an angle BCD , equal to BCA , but on the opposite side ... angles are equal . Consequently AC = D B. But the triangles also have ∠ABC , ACB , and side BC respectively equal ...
... opposite side of B C. A D Also suppose CD to make with BC an angle BCD , equal to BCA , but on the opposite side ... angles are equal . Consequently AC = D B. But the triangles also have ∠ABC , ACB , and side BC respectively equal ...
Página 48
... opposite angles . 18. The perimeter of a triangle is less than double the sum of the three middle lines . 19. The ... opposite sides of a line E F , are joined with a point Cin EF . Prove that the difference between AC and BC is ...
... opposite angles . 18. The perimeter of a triangle is less than double the sum of the three middle lines . 19. The ... opposite sides of a line E F , are joined with a point Cin EF . Prove that the difference between AC and BC is ...
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Modern Geometry [Ed.] with an Appendix by W.B. Jack Richard Wormell Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD adjacent angles alternate angles angles equal angular points base bisect bisector CBEF centre chord circumference circumscribing circle common measure Construct a triangle contra-positive converse describe a circle diagonals diameter distance divided draw a straight equal angles equidistant extremities figure Find the area given circle given point given straight line gonals greater half Hence hypothenuse inches incommensurable inscribed circle interior angles isosceles triangle less Let ABC line drawn locus of points magnitudes middle points number of sides number of units parallel parallelogram pentagon perimeter perpendicular point of intersection proportion propositions proved quadrilateral radii radius ratio rect rectangle contained regular polygon respectively equal rhombus right angles right-angled triangle secant segment semicircle side opposite similar similar triangles square tangent termed Theo theodolite THEOREMS ON CHAPTER three given touch triangles are equal vertex vertical angle دو دو دو
Pasajes populares
Página 242 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 240 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Página 240 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Página 242 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.
Página 242 - If from the vertical angle of a triangle a straight line be drawn perpendicular to the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle.
Página 241 - If the first has to the second the same ratio which the third has to the fourth...
Página 240 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 242 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Página 239 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.