Plane Geometry: With Problems and ApplicationsAllyn and Bacon, 1910 - 280 páginas |
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Página 11
... Hypotenuse Select each kind from the figures on this page . The side of a right triangle opposite the right angle is called the hypotenuse in dis- tinction from the other two sides , which are sometimes called its legs . 24. The side ...
... Hypotenuse Select each kind from the figures on this page . The side of a right triangle opposite the right angle is called the hypotenuse in dis- tinction from the other two sides , which are sometimes called its legs . 24. The side ...
Página 35
... hypotenuse of a right triangle is greater than either leg . 2. Show that not more than two equal line - segments can be drawn from a point to a straight line . SUGGESTION . Suppose a third drawn . Then apply §§ 37 , 83 , 84 . 3. Show by ...
... hypotenuse of a right triangle is greater than either leg . 2. Show that not more than two equal line - segments can be drawn from a point to a straight line . SUGGESTION . Suppose a third drawn . Then apply §§ 37 , 83 , 84 . 3. Show by ...
Página 41
... hypotenuse and an acute angle of one are equal respectively to the hypotenuse and an acute angle of the other , the triangles are congruent . Prove in full . 8. Can a triangle have two right angles ? Two obtuse angles ? Can the sum of ...
... hypotenuse and an acute angle of one are equal respectively to the hypotenuse and an acute angle of the other , the triangles are congruent . Prove in full . 8. Can a triangle have two right angles ? Two obtuse angles ? Can the sum of ...
Página 43
... hypotenuse and one side of the other , the triangles are congruent . B B ' B A CA C ' A C A ' Given the right BC = B'C ' . ABC and A'B'C ' , having AB = A'B ' and To prove that △ ABC ≃ △ A'B'C ' . Proof : Place the triangles so that ...
... hypotenuse and one side of the other , the triangles are congruent . B B ' B A CA C ' A C A ' Given the right BC = B'C ' . ABC and A'B'C ' , having AB = A'B ' and To prove that △ ABC ≃ △ A'B'C ' . Proof : Place the triangles so that ...
Página 65
... hypotenuse is twice as long as one side , then one acute angle is 60 ° and the other 30 ° . SUGGESTION . Let D be the middle point of AB . Use Ex . 12 and the hypothesis to show that equilateral . D B ACD is A E C Prove the converse by ...
... hypotenuse is twice as long as one side , then one acute angle is 60 ° and the other 30 ° . SUGGESTION . Let D be the middle point of AB . Use Ex . 12 and the hypothesis to show that equilateral . D B ACD is A E C Prove the converse by ...
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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,