Plane GeometryMacmillan, 1901 |
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Αποτελέσματα 1 - 5 από τα 25.
Σελίδα vi
... equal triangles ; the method of proving the propor- tionality of lines by means of similar triangles , etc. , and finally the analyses of theorems and problems are introduced , but in a more concrete form than usual . The propositions ...
... equal triangles ; the method of proving the propor- tionality of lines by means of similar triangles , etc. , and finally the analyses of theorems and problems are introduced , but in a more concrete form than usual . The propositions ...
Σελίδα xii
... equal to . ax . • • is equivalent to . circum . • • alternate . axiom . circumference ... similar . hy . · · • hypotenuse . • • angle . hyp . • • hypothesis . · angles . int . • interior . • Δ A • triangle . isos . · isosceles . · triangles ...
... equal to . ax . • • is equivalent to . circum . • • alternate . axiom . circumference ... similar . hy . · · • hypotenuse . • • angle . hyp . • • hypothesis . · angles . int . • interior . • Δ A • triangle . isos . · isosceles . · triangles ...
Σελίδα 13
... Similar abbreviations will be suggested for other propositions . 71. DEF . Polygons are mutually equiangular if their angles are respectively equal , and ... triangles . PROPOSITION III . THEOREM 72. Two triangles are equal if TRIANGLES 13.
... Similar abbreviations will be suggested for other propositions . 71. DEF . Polygons are mutually equiangular if their angles are respectively equal , and ... triangles . PROPOSITION III . THEOREM 72. Two triangles are equal if TRIANGLES 13.
Σελίδα 48
... different triangles , Prop . XXX is used . In some cases several methods will lead to the desired result . The inequality of angles is proved in a similar manner by Props . IV , XXVIII and Prop . XXXI . Ex . 177. If AD and BC intersect ...
... different triangles , Prop . XXX is used . In some cases several methods will lead to the desired result . The inequality of angles is proved in a similar manner by Props . IV , XXVIII and Prop . XXXI . Ex . 177. If AD and BC intersect ...
Σελίδα 51
... equal , the figure is a parallelogram . A B Hyp . To prove D In quadrilateral ABDC AB : = CD ; AD = BC . AD || BC ; AB || CD . HINT . - Prove the equality of a pair of alternate interior angles by means of equal triangles . Ex . 192. If ...
... equal , the figure is a parallelogram . A B Hyp . To prove D In quadrilateral ABDC AB : = CD ; AD = BC . AD || BC ; AB || CD . HINT . - Prove the equality of a pair of alternate interior angles by means of equal triangles . Ex . 192. If ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AABC ABCD adjacent angles algebraic altitude angle equal angle formed angles are equal apothem base angle bisect bisector central angle circumference construct a triangle decagon diagonals diagram for Prop diameter draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle find a point Find the area given circle given line given point given triangle HINT homologous sides hypotenuse inscribed isosceles triangle joining the midpoints line joining mean proportional measured by arc median opposite sides parallel lines parallelogram perimeter perpendicular perpendicular-bisector point equidistant produced proof is left PROPOSITION prove Proof proving the equality quadrilateral radii rectangle regular hexagon regular polygon rhombus right angle right triangle SCHOLIUM School secant segments side equal similar polygons similar triangles straight angle straight line tangent THEOREM third side transversal trapezoid triangle ABC triangle are equal vertex vertical angle
Δημοφιλή αποσπάσματα
Σελίδα 148 - 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 180 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. B' ADC A' D' C' Hyp. In triangles ABC and A'B'C', ZA = ZA'.
Σελίδα 45 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 31 - The median to the base of an isosceles triangle is perpendicular to the base.
Σελίδα 209 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Σελίδα 130 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Σελίδα 71 - The midpoints of two opposite sides of a quadrilateral and the midpoints of the diagonals determine the vertices of a parallelogram. * Ex.
Σελίδα 26 - If one angle of a triangle is equal to the sum of the other two, the triangle can be divided into two isosceles triangles.
Σελίδα 190 - The areas of two similar triangles are to each other as the squares of any two homologous sides.
Σελίδα 56 - A line which joins the midpoints of two sides of a triangle is parallel to the third side and equal to half of it.