...AE. we have But 4JiE is the square of 2.AE or of .-1C ; and A In. is the square BD ; therefore the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. THEOREM. Fig 114. 196. The line DE (fig. 114), drawn parallel to the base...

...BC = 4AE + IDE. But 4AE is the square of 2AE or of AC; and 4DE is the square of BD ; therefore the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. THEOREM. Fig. 114. 196. The line DE (fig. 114), drawn parallel to the base...

...BC- 4AE + 4DE. But 4.4JU is the square of <2JLE or of AC; and 4DE is the square of BD ; therefore the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. THEORKM. Fig. 114. 1 96. The line DE (fig. 1 1 4), drawn parallel to the...

...IDE. 2 2 • But 4AE is the square of 2.4£ or of AC; and 4DE is the square of BD ; therefore the su;n of the squares of the sides of a parallelogram is equal to the sum of the squares- f the diagonals. THEOREM. Fig. 114. 1 96. Tlie line DE (fig. 1 1 4), drawn parallel to the...

...squares of BF and DF is equal to twice that of EF and D E. Hence the proposition is manifest. (301) The sum of the squares of the sides of a parallelogram is equal to that of the diagonals. For in that case the line EF vanishes, since the diagonals bisect each other...

...with twice the square of BC ; because CP and BC are equal. Fig: 7. Schol. Hence it is evident that the sum of the squares of the sides of a parallelogram is equal to the (i)Prcp.29. sum of the squares of the diagonals. B- 1- Because the angles DEC and BDA, ACB and CAD...

...+ BC = 4AE + 4DE. But 4AE is the square of 2AE or ofAC; and 4DEis the square of BD ; therefore the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. THEOREM. Fig 114. 196. The line DE (fig. 114), drawn parallel to the lose...

...is equal to the square on AB, together with twice the square on BC. 147. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 148. The base of a triangle is given and is bisected by the centre of a given...

...is equal to the square on AB, together with twice the square on BC. 147. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 148. The base of a triangle is given and is bisected by the centre of a given...

...equal to AC', and 4.DE2 to BD' (P. Vin., C.) : hence, AB2 + BC2 + CD2 + DA2 = AC2 + BD'. That is, the sum of the squares of the sides of a parallelogram, is equal to the sum of the squares of its diagonals. / ^ PROPOSITION XV. THEOREM. In any triangle, a line drawn parallel to the...