Elements of Plane GeometryAmerican Book Company, 1901 - 247 Seiten |
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Seite 8
... Square , 194 Straight line , 6 determined , 246 divided externally , 506 divided harmonically , 509 Quadrant , 346 Quadrilateral , 152 Quantities , commensurable , 342 constant , 340 incommensurable , 342 variable , 340 Radius , 20 ...
... Square , 194 Straight line , 6 determined , 246 divided externally , 506 divided harmonically , 509 Quadrant , 346 Quadrilateral , 152 Quantities , commensurable , 342 constant , 340 incommensurable , 342 variable , 340 Radius , 20 ...
Seite 58
... square is an equilateral rectangle ; and a rhombus is an equilateral rhomboid . PROPOSITION XXXII . THEOREM 195. The opposite sides of a parallelogram are equal ; and conversely , if the opposite sides of a quadrilateral are equal , the ...
... square is an equilateral rectangle ; and a rhombus is an equilateral rhomboid . PROPOSITION XXXII . THEOREM 195. The opposite sides of a parallelogram are equal ; and conversely , if the opposite sides of a quadrilateral are equal , the ...
Seite 61
... square B , 1. Are equal . 2. Bisect each other . 3. Are perpendicular to each other . 4. Bisect the angles of the square . 209. COROLLARY II . The diagonals of a rhombus 1. Are unequal . 2. Bisect each other . 3. Are perpendicular to ...
... square B , 1. Are equal . 2. Bisect each other . 3. Are perpendicular to each other . 4. Bisect the angles of the square . 209. COROLLARY II . The diagonals of a rhombus 1. Are unequal . 2. Bisect each other . 3. Are perpendicular to ...
Seite 62
... square 1. Are equal . 2. Bisect each other . 3. Are not perpendicular to each other . 4. Do not bisect the angles of the rec- tangle . B To prove that the diagonals are not perpendicular to each other , apply § 182 to A BOC and COD ...
... square 1. Are equal . 2. Bisect each other . 3. Are not perpendicular to each other . 4. Do not bisect the angles of the rec- tangle . B To prove that the diagonals are not perpendicular to each other , apply § 182 to A BOC and COD ...
Seite 72
... square ABCD , the equal distances AE , BF , CG , and DH are laid off . Prove that the quadrilateral EFGH is also a square . E B Α H O G 16. The perpendiculars erected to the sides of a triangle 72 PLANE GEOMETRY.
... square ABCD , the equal distances AE , BF , CG , and DH are laid off . Prove that the quadrilateral EFGH is also a square . E B Α H O G 16. The perpendiculars erected to the sides of a triangle 72 PLANE GEOMETRY.
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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.