Plane Geometry: With Problems and ApplicationsAllyn and Bacon, 1910 - 280 páginas |
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Página 2
... Hence , Two straight lines cannot have more than one point in common unless they coincide and are the same line ; that is , two points determine a straight line . This would not be so if the lines had width , as may be seen by examining ...
... Hence , Two straight lines cannot have more than one point in common unless they coincide and are the same line ; that is , two points determine a straight line . This would not be so if the lines had width , as may be seen by examining ...
Página 13
... Hence if we make a pattern of a figure , say on tracing paper , and then make a second figure from this pattern , the two figures are congruent to each other . 29. If △ ABC = A'B'C ' , the notation of the triangles may be so arranged ...
... Hence if we make a pattern of a figure , say on tracing paper , and then make a second figure from this pattern , the two figures are congruent to each other . 29. If △ ABC = A'B'C ' , the notation of the triangles may be so arranged ...
Página 14
... Hence , side BC will coincide with B'C ' ( § 8 ) . Thus , the two triangles coincide throughout and hence are congruent ( § 27 ) . The process just used is called superposition . It BT may sometimes be necessary to move a figure out of ...
... Hence , side BC will coincide with B'C ' ( § 8 ) . Thus , the two triangles coincide throughout and hence are congruent ( § 27 ) . The process just used is called superposition . It BT may sometimes be necessary to move a figure out of ...
Página 16
... hence C must lie on the ray в'с ' . Since the point clies on both of the rays A'C ' and B'C ' , it must lie at their point of intersection c ' ( § 5 ) . Hence , the triangles coincide and are , therefore , congruent ( § 27 ) . 36 ...
... hence C must lie on the ray в'с ' . Since the point clies on both of the rays A'C ' and B'C ' , it must lie at their point of intersection c ' ( § 5 ) . Hence , the triangles coincide and are , therefore , congruent ( § 27 ) . 36 ...
Página 19
... Hence , △ ABC ' ABC A'B'C ' . A'B'C ' . ( § 26 ) ( § 28 ) Make an outline of the steps in the above argument , and see that each step is needed in deriving the next . 41. Definition . If one triangle is congruent to another because ...
... Hence , △ ABC ' ABC A'B'C ' . A'B'C ' . ( § 26 ) ( § 28 ) Make an outline of the steps in the above argument , and see that each step is needed in deriving the next . 41. Definition . If one triangle is congruent to another because ...
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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,