 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...diagonals of a parallelogram are equal, the figure is a rectangle. PROPOSITION XXXIV. THEOREM 146. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. B— Given quadrilateral A BCD, with AB = CD; AD = BC. To prove AD II BC; AB II CD. Ex. 347. If the... | |
 | John Wesley Young, Albert John Schwartz - Geometry, Modern - 1915 - 250 pages
...parallelogram ABCD, BE and DF are perpendicular to the diagonal AC. Prove that BE = DF. 244. THEOREM. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. FIG. 106. (The proof is left to the student.) SUGGESTION : Draw a diagonal BD. A ABD = A CBD. Show... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...diagonal of a parallelogram divides it into two congruent triangles. PROPOSITION XXXIX. THEOREM 128. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. [Converse of 124.] Given : Quadrilateral ABCD ; AB = DC; AD=BC. To Prove : ABCD is a O. Proof : Draw... | |
 | John Charles Stone, James Franklin Millis - Geometry - 1916 - 306 pages
...consecutive angles supplementary. The proof is left to the student. Write the proof in full. 87. Theorem. — If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. A Hypothesis. In quadrilateral AB CD, AB = DC and AD = BC. Conclusion. AB CD is a parallelogram. Suggestions.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...same diagram, if AB = ED, A. AF=DC, AF\\DC, and AD is a st. line, then BC is parallel to FE. Ex. 245. If two sides of a quadrilateral are equal and parallel, the other two sides are parallel. D e A '~ Ex. 246. In the diagram given here, if AB II CD, AD\\BC, AE-FC, and AC in a st.... | |
 | Claude Irwin Palmer - Geometry, Solid - 1918 - 192 pages
...bisect each other. § 168. Theorem. Parallels cut off by two parallel lines are equal. § 169. Theorem. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. § 160. Theorem. If two opposite sides of a quadrilateral are equal and parallel, the figure is a parallelogram.... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry - 1918 - 460 pages
...equal, \ \ H JK AB II CD and EF II HK. C - j? - ^- o jl Prove that EF = HK. §155 A c F 159. Theorem. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. AB Given AB = DC, and AD = BC. /-^X 7 To prove that ABCD is a parallelogram. / >-y Proof. Draw the... | |
 | George Albert Wentworth, David Eugene Smith, Joseph Clifton Brown - Mathematics - 1918 - 304 pages
...diagonal determined by the other vertices, are equal. THEOREM. OPPOSITE SIDES EQUAL 96. If both pairs of opposite sides of a quadrilateral are equal, the figure is a parallelogram. Given the quadrilateral ABCD, having BC equal to AD, and AB equal to DC. To prove that ABCD is a parallelogram.... | |
 | High schools - 1919 - 962 pages
...bisector of the vertex angle of a triangular is perpendicular to the base, the triangle is isosceles. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.) In preparation for a recitation in geometry, I make an assignment to be •worked out in a forty-five... | |
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If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 
