Plane Geometry: With Problems and ApplicationsAllyn and Bacon, 1910 - 280 páginas |
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Página 12
... congruent if , without changing the shape or size of either , they may be so placed as to coincide throughout . This is denoted by the symbol , read is congruent to . ~ || 2 In the case of line - segments and angles , congruence is ...
... congruent if , without changing the shape or size of either , they may be so placed as to coincide throughout . This is denoted by the symbol , read is congruent to . ~ || 2 In the case of line - segments and angles , congruence is ...
Página 13
... congruent to the same figure they are congruent to each other . 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 ...
... congruent to the same figure they are congruent to each other . 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 ...
Página 14
... congruent by making a pattern of one and applying it to the other is often inconvenient or impossible . There are other methods in which it is necessary only to determine whether certain sides and angles are equal . These methods are ...
... congruent by making a pattern of one and applying it to the other is often inconvenient or impossible . There are other methods in which it is necessary only to determine whether certain sides and angles are equal . These methods are ...
Página 15
... congruent ? Illustrate by constructing two such triangles . 4. Show by the test of § 32 that two right triangles are congruent if the legs of one are equal respectively to the legs of the other . Can this be shown directly by ...
... congruent ? Illustrate by constructing two such triangles . 4. Show by the test of § 32 that two right triangles are congruent if the legs of one are equal respectively to the legs of the other . Can this be shown directly by ...
Página 16
... congruent . This is shown by the following argument : C A B C ' A ' B ' Let ABC and A'B'C ' be two triangles in which ∠A = ∠A ' , ∠B = ∠B ' , and AB = A'B ' . We are to show that △ ABC ≥ △ A'B'C ' . Place △ ABC upon △ A'B'C ...
... congruent . This is shown by the following argument : C A B C ' A ' B ' Let ABC and A'B'C ' be two triangles in which ∠A = ∠A ' , ∠B = ∠B ' , and AB = A'B ' . We are to show that △ ABC ≥ △ A'B'C ' . Place △ ABC upon △ A'B'C ...
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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,