Elements of Plane GeometryAmerican Book Company, 1901 - 247 Seiten |
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Ergebnisse 1-5 von 36
Seite 8
... third , 404 Proposition , 24 Sides of angle , 13 of triangle , 18 Similar arcs , 787 polygons , 477 sectors , 787 segments , 787 Similitude , center of , 556 Solid , geometrical , 2 Square , 194 Straight line , 6 determined , 246 ...
... third , 404 Proposition , 24 Sides of angle , 13 of triangle , 18 Similar arcs , 787 polygons , 477 sectors , 787 segments , 787 Similitude , center of , 556 Solid , geometrical , 2 Square , 194 Straight line , 6 determined , 246 ...
Seite 36
... 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 plane , if they are not parallel they must meet . If they do meet we should ...
... 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 plane , if they are not parallel they must meet . If they do meet we should ...
Seite 46
... third can be found by subtracting their sum from two right angles . 140. COROLLARY II . If two angles of one triangle are equal respectively to two angles of another , the third angles are equal , and the triangles are mutually ...
... third can be found by subtracting their sum from two right angles . 140. COROLLARY II . If two angles of one triangle are equal respectively to two angles of another , the third angles are equal , and the triangles are mutually ...
Seite 50
... third side , but the difference of two sides of a triangle is less than the third side . B E A Let C F ABC be any A. To Prove AB + BC > AC . Proof . Apply axiom 14 . Q.E.D. Let DEF be any A. To Prove DE - EF < DF . Proof . DE DF EF ...
... third side , but the difference of two sides of a triangle is less than the third side . B E A Let C F ABC be any A. To Prove AB + BC > AC . Proof . Apply axiom 14 . Q.E.D. Let DEF be any A. To Prove DE - EF < DF . Proof . DE DF EF ...
Seite 51
... third side lie ? 171. EXERCISE . Each side of a triangle is less than the semi- perimeter . 172. EXERCISE . The sum of the lines drawn from a point within a triangle to the three ver- tices is greater than the semi - perimeter . Prove ...
... third side lie ? 171. EXERCISE . Each side of a triangle is less than the semi- perimeter . 172. EXERCISE . The sum of the lines drawn from a point within a triangle to the three ver- tices is greater than the semi - perimeter . Prove ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
Seite 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.
Seite 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.
Seite 221 - Tangents to a circle at the middle points of the arcs subtended by the sides of a regular inscribed polygon...
Seite 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.
Seite 61 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.