Plane Geometry: With Problems and ApplicationsAllyn and Bacon, 1910 - 280 páginas |
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Página 31
... proof ( see § 60 ) . Thus Aristotle ( 384-322 в.с. ) says : " Every demonstration must start from undemonstrable ... full detail . This should be done in the shortest possi- ble sentences , usually giving a separate line to each ...
... proof ( see § 60 ) . Thus Aristotle ( 384-322 в.с. ) says : " Every demonstration must start from undemonstrable ... full detail . This should be done in the shortest possi- ble sentences , usually giving a separate line to each ...
Página 32
... proof of the following theorem is shown in full detail as it should be written by the pupil or given orally , except that the numbers of paragraphs should not be required . 83. THEOREM . An exterior angle of a triangle is greater than ...
... proof of the following theorem is shown in full detail as it should be written by the pupil or given orally , except that the numbers of paragraphs should not be required . 83. THEOREM . An exterior angle of a triangle is greater than ...
Página 33
... proof and give it in full . Hereafter more and more of the details of the proofs will be left for the student to fill in . When reference is made to a paragraph in the text or when the reason for a step is called for , the complete ...
... proof and give it in full . Hereafter more and more of the details of the proofs will be left for the student to fill in . When reference is made to a paragraph in the text or when the reason for a step is called for , the complete ...
Página 39
... proof in full . Of what theorem is this the converse ? 100 . EXERCISES . 3 1 $ 1. State and prove the converse of the theorem in § 92 . 2 -1 2 2. Prove that if two parallel lines are cut by a transversal the alternate exterior angles ...
... proof in full . Of what theorem is this the converse ? 100 . EXERCISES . 3 1 $ 1. State and prove the converse of the theorem in § 92 . 2 -1 2 2. Prove that if two parallel lines are cut by a transversal the alternate exterior angles ...
Página 41
... proof is left to the student . Compare this theorem with that of § 83 . 104. Definition . A theorem which follows ... full . 8. Can a triangle have two right angles ? Two obtuse angles ? Can the sum of two angles of a triangle be ...
... proof is left to the student . Compare this theorem with that of § 83 . 104. Definition . A theorem which follows ... full . 8. Can a triangle have two right angles ? Two obtuse angles ? Can the sum of two angles of a triangle be ...
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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,