Elements of Plane GeometryAmerican Book Company, 1901 - 247 σελίδες |
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Αποτελέσματα 1 - 5 από τα 41.
Σελίδα 13
... prolonged to any length . 3. If two lines are unequal , the length of the smaller can be laid off on the larger . 4. A circumference can be described with any point as a center , and with a radius of any length . SYMBOLS AND ...
... prolonged to any length . 3. If two lines are unequal , the length of the smaller can be laid off on the larger . 4. A circumference can be described with any point as a center , and with a radius of any length . SYMBOLS AND ...
Σελίδα 27
... Prolong one of the lines , as OE , to G. Then apply § 63 to the angles on each side of GE . 65. DEFINITION . If two angles are together equal to two right angles , they are called supplemen- tary angles . Each angle is the sup- plement ...
... Prolong one of the lines , as OE , to G. Then apply § 63 to the angles on each side of GE . 65. DEFINITION . If two angles are together equal to two right angles , they are called supplemen- tary angles . Each angle is the sup- plement ...
Σελίδα 33
... Prolong CD until DF = CD , and draw EF . Prove CDE and FDE equal in all respects . Whence 21 = 22 . But 21 = 1 R.A. by supposition . Show that 21 + 22 = 2 R.A.'s . If the sum of angles 1 and 2 is two R.A.'s , CE and EF form a straight ...
... Prolong CD until DF = CD , and draw EF . Prove CDE and FDE equal in all respects . Whence 21 = 22 . But 21 = 1 R.A. by supposition . Show that 21 + 22 = 2 R.A.'s . If the sum of angles 1 and 2 is two R.A.'s , CE and EF form a straight ...
Σελίδα 36
... prolonged . PROPOSITION XVI . THEOREM 108. If two lines are parallel to a third line , they are parallel to each other . A C B D E- Let AB and CD be to EF . To Prove AB and CD to each other . Proof . Since AB and CD are in the same ...
... prolonged . PROPOSITION XVI . THEOREM 108. If two lines are parallel to a third line , they are parallel to each other . A C B D E- Let AB and CD be to EF . To Prove AB and CD to each other . Proof . Since AB and CD are in the same ...
Σελίδα 39
... prolong MH until it meets AB in some point G. Prove the AGMO and MSH equal in all respects . Whence LH = / G. LH is by construction a R.A. .. G is a R.A. AB and CD are parallel . ( ? ) Q.E.D. 116. COROLLARY . If two lines are cut by a ...
... prolong MH until it meets AB in some point G. Prove the AGMO and MSH equal in all respects . Whence LH = / G. LH is by construction a R.A. .. G is a R.A. AB and CD are parallel . ( ? ) Q.E.D. 116. COROLLARY . If two lines are cut by a ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AABC AB² ABC and DEF AC² adjacent angles altitudes angle formed angles equal apothem arc ABC arcs intercepted BC² bisector chord circles are tangent circum circumference Construct a triangle COROLLARY DEFINITION Describe a circle diagonals diameter divided EFGH equal circles equally distant equiangular polygon equilateral triangle EXERCISE exterior angles figure given angle given circle given line given point homologous homologous sides hypotenuse inscribed angle isosceles triangle joining the middle Let ABC Let To Prove line joining mean proportional medians meet middle points mutually equiangular opposite sides parallelogram passes perimeter perpendicular point of intersection prolonged PROPOSITION Prove ABCD Prove Proof quadrilateral ratio rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons similar triangles straight line tangent THEOREM trapezoid triangle ABC unequal vertex vertical angle Whence ΔΑΒΟ ᎠᏴ
Δημοφιλή αποσπάσματα
Σελίδα 68 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Σελίδα 163 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Σελίδα 120 - If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair.
Σελίδα 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
Σελίδα 203 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Σελίδα 15 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Σελίδα 221 - Tangents to a circle at the middle points of the arcs subtended by the sides of a regular inscribed polygon...
Σελίδα 11 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the center.
Σελίδα 61 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.