Plane Geometry: With Problems and ApplicationsAllyn and Bacon, 1910 - 280 páginas |
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Página 77
... number of equilateral triangles exactly cover the whole plane about the vertices ? Why ? ( c ) Do the triangles that meet in one point form a regular hexagon ? ( d ) At what angle to the horizontal lines are the oblique lines that form ...
... number of equilateral triangles exactly cover the whole plane about the vertices ? Why ? ( c ) Do the triangles that meet in one point form a regular hexagon ? ( d ) At what angle to the horizontal lines are the oblique lines that form ...
Página 78
... How many such hexagons meet in a point ? Will this number exactly cover the plane about the point ? Why ? 6. Point ... sides in order form a parallelogram , and the four triangles thus cut off may be pieced together to form another ...
... How many such hexagons meet in a point ? Will this number exactly cover the plane about the point ? Why ? 6. Point ... sides in order form a parallelogram , and the four triangles thus cut off may be pieced together to form another ...
Página 79
... sides . Can any regular polygon of more than six sides be used to form a complete pavement ? Note that the larger the number of sides of a regular polygon the larger is each angle . 16. A carpenter divides a board into strips of equal ...
... sides . Can any regular polygon of more than six sides be used to form a complete pavement ? Note that the larger the number of sides of a regular polygon the larger is each angle . 16. A carpenter divides a board into strips of equal ...
Página 108
... number of degrees in the arcs into which the points of tangency divide the circle . 7. Divide each side of an ... sides of the hexagon are tangent to the circle . SUGGESTION . Show that the perpendicular bisec- tors of the segments ...
... number of degrees in the arcs into which the points of tangency divide the circle . 7. Divide each side of an ... sides of the hexagon are tangent to the circle . SUGGESTION . Show that the perpendicular bisec- tors of the segments ...
Página 133
... number of chords are drawn , the product of the segments of one chord is equal to the product of the seg- ments of ... sides ? BP PD Show that EP PA Complete the proof . It follows from this theorem that if a chord AB is made to ...
... number of chords are drawn , the product of the segments of one chord is equal to the product of the seg- ments of ... sides ? BP PD Show that EP PA Complete the proof . It follows from this theorem that if a chord AB is made to ...
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Términos y frases comunes
ABCD acute angle adjacent angles altitude angle formed angles are equal apothem axes of symmetry axioms base bisects called central angle chord circle tangent circumscribed coincide congruent corresponding sides Definition diagonal diameter distance divided dodecagon Draw drawn equal angles equal circles equiangular equilateral triangle EXERCISES exterior angle figure Find the area Find the locus Find the radius fixed point geometric Give the proof given point given segment given triangle Hence hypotenuse hypothesis inches inscribed intersection isosceles trapezoid isosceles triangle l₁ length line-segment measure meet middle points number of sides Outline of Proof parallel lines parallelogram perigon perimeter plane proof in full quadrilateral radii ratio rectangle regular hexagon regular octagon regular polygon rhombus right angles right triangle secant semicircle Show shown square straight angle straight line subtend SUGGESTION THEOREM trapezoid triangle ABC vertex vertices width
Pasajes populares
Página 223 - If two triangles have two sides of the one equal to two sides of the other...
Página 41 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Página 121 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Página 60 - 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 46 INTERCEPTS BY PARALLEL LINES.
Página 182 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems.
Página 161 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Página 227 - Find the locus of a point such that the difference of the squares of its distances from two fixed points is a constant.
Página 210 - The area of a rectangle is equal to the product of its base and altitude.
Página 31 - Kuclid divided unproved propositions into two classes: axioms, or "common notions," which are true of all things, such as, " If things are equal to the same thing they are equal to each other"; and postulates, which apply only to geometry, such as,