# Lessons on form, for teachers [of geometry].

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Page 36 - The square described on the hypothenuse of a rightangled triangle is equal to the sum of the squares described on the other two sides.
Page 39 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Page 39 - In any triangle, the square of a side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other side upon it.
Page 33 - Parallelograms on the same base, or on equal bases, and between the same parallels, are equal.
Page 24 - Two triangles which are such that the sides and angles of the one are equal respectively to the sides and angles of the other will be called congruent. If ABC be congruent with A'B'C', we shall express the fact by the notation : A ABC = A A'B'C'.
Page 21 - Since the three angles of the triangle ABC are equal to two right angles, .-.the angles DAB, DBA, DCF are together equal to one right angle, ie to DCF, and CDF; whence the two angles DAB, DBA are together...
Page 25 - EQUAL. 304. Theorem. — Two triangles are similar, when the three angles of the one are respectively equal to the three angles of the other. This may appear to be only a case of the definition of similar figures; but it may be shown that every angle that can be made by any lines whatever in the one, may have its corresponding equal and similarly situated angle in the other. Let the angles A, B, and C be respectively equal to the angles...
Page 76 - Through three points not in the same straight line, one and only one plane can be passed.
Page 36 - To find an extreme, divide the product of the means by the given extreme. To find a mean, divide the product of the extremes by the given mean.