Plane Geometry: With Problems and ApplicationsAllyn and Bacon, 1910 - 280 páginas |
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Página 23
... proof as shown by such an outline is of great importance in master ing it . 53 . EXERCISES . 1. In the construction of § 51 , is it necessary to use the same radius in locating the points C and D ? 2. Name the isosceles triangles in the ...
... proof as shown by such an outline is of great importance in master ing it . 53 . EXERCISES . 1. In the construction of § 51 , is it necessary to use the same radius in locating the points C and D ? 2. Name the isosceles triangles in the ...
Página 62
... Proof : The figure ACGE is a parallelogram or a trapezoid according as t1ll t2 or not . In either case BF , which ... Outline of Proof : Through each vertex of the given triangle ABC draw a line parallel to the opposite side ...
... Proof : The figure ACGE is a parallelogram or a trapezoid according as t1ll t2 or not . In either case BF , which ... Outline of Proof : Through each vertex of the given triangle ABC draw a line parallel to the opposite side ...
Página 63
... Outline of Proof : Taking Fand G , the middle points of OB and OA respectively , use §§ 151 and 144 to show that the figure GFED is a parallelogram , and hence that DO = OF = FB and EO = OG = GA . That is , o trisects AE and BD . In the ...
... Outline of Proof : Taking Fand G , the middle points of OB and OA respectively , use §§ 151 and 144 to show that the figure GFED is a parallelogram , and hence that DO = OF = FB and EO = OG = GA . That is , o trisects AE and BD . In the ...
Página 67
... Outline of Proof : angles is 2 nrt . 4 . The sum of both exterior and interior ( Why ? ) The sum of the interior angles is ( 2 n – 4 ) rt . 4. ( Why ? ) Hence , the sum of the exterior angles is 4 rt . 4. ( Why ? ) Write out the proof ...
... Outline of Proof : angles is 2 nrt . 4 . The sum of both exterior and interior ( Why ? ) The sum of the interior angles is ( 2 n – 4 ) rt . 4. ( Why ? ) Hence , the sum of the exterior angles is 4 rt . 4. ( Why ? ) Write out the proof ...
Página 71
... Outline of Proof : It is to be shown that for every point P in the figure , a point P " also in the figure can be found such that Po = P " O and POP " is a 12 straight line . Draw PP ' 1 l , P'P " ᅩ ' , P " P " " " Il and connect the ...
... Outline of Proof : It is to be shown that for every point P in the figure , a point P " also in the figure can be found such that Po = P " O and POP " is a 12 straight line . Draw PP ' 1 l , P'P " ᅩ ' , P " P " " " Il and connect the ...
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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,