A Study in the Psychology of Learning in Geometry

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Teachers college, Columbia university, 1925 - Geometry - 60 pages
 

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Page 49 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Page 57 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.
Page 54 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Page 15 - Two triangles are equal if two sides and the median to one of these sides are equal respectively to two sides and the homologous median of the other. Ex.
Page 42 - Prove that a line from the vertex of an isosceles triangle to the mid-point of the base is perpendicular to the base.
Page 52 - If two right triangles have the hypotenuse and a leg of one equal respectively to the hypotenuse and a leg of the other, the triangles are congruent, (rt. A h. 1.) C" Given the right triangles ABC and A'B'C', with the hypotenuse AB equal to the hypotenuse A'B', and with AC equal to A'C'.
Page 42 - Any point in the bisector of the vertical angle of an isosceles triangle is equidistant from the extremities of the base (Ex. 34, § 160). Ex. 38. If the bisector of an angle of a triangle is perpendicular to the opposite side, the triangle is isosceles.
Page 42 - The bisector of the angle at the vertex of an isosceles triangle bisects the base and is perpendicular to the base.
Page 16 - If the median of a triangle is equal to half the side to which it is drawn, it is a right triangle.
Page 8 - One ambitious proposal of the kind consists of a set of questions which a pupil tackling a geometry "original" is supposed to ask himself. (1) What kind of relation is to be proved? (2) Is there any part of the figure about which we know two or more facts? (3) Draw the figure. (4) State what relations are given. (5) State what relations are to be proved. (6) What is the link that may connect (4) and (5) ? (7) Test the latter conclusion. (8) If true, write the proof and if not consider other suggestions....

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