 | Education - 1902 - 880 pages
...accepted. First i Define hypothesis, locus of a point, altitude, diamdivision eterj rhomboid. 2 Prove that if the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 3 Prove that two mutually equiangular triangles are similar. 4 Prove that in the same circle or in... | |
 | Alan Sanders - Geometry - 1903 - 392 pages
...rhomboid. PROPOSITION XXXII. THEOREM 195. The opposite sides of a parallelogram, are equal; and conversely, if the opposite sides of a quadrilateral are equal, the figure is a parallelogram. Let ABCD be a parallelogram. To prove AB = CD and BC = AD. Proof. Draw the diagonal BD. Show that A... | |
 | George Albert Wentworth - Geometry - 1904 - 496 pages
...181. COR. 3. Two parallel lines are everywhere equally distant. D PROPOSITION XXXIV. THEOREM. 182. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. Let the figure ABCE be a quadrilateral, having BC equal to AE and AB to EC. To prove that the figure... | |
 | Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...equal. 158. COR. 3. Two parallel lines are everywhere equidistant. _ PROPOSITION XXXIV. THEOREM 159. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. Given the quadrilateral ABCD in which AB=CD and BC=AD. To prove ABCD a ZZ7 . Proof. Draw the diagonal... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...PARALLELOGRAMS. i. If one angle of a parallelogram is a right angle, all its angles are right angles. 2. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 3. If the opposite angles of a quadrilateral are equal, the figure is a parallelogram. 4. If a quadrilateral... | |
 | William Chauvenet - 1905 - 336 pages
...opposite sides of a quadrilateral are equal and parallel, the figure is a parallelogram. PROPOSITION XXXI. If the opposite sides of a quadrilateral are equal, the figure Is a varallelogram. PROPOSITION XXXII. The diagonals of a parallelogram bisect each other. BOOK II. PROPOSITIONS.... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1906 - 268 pages
...equal triangles. 133. COR. The opposite angles of a parallelogram are equal. (See 27.) 134. THEOREM. If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. [Converse of 130.] Given: Quadrilateral AB CD; AB = DC ; AD = BC. To Prove : ABCD is a O. Proof : Draw... | |
 | Isaac Newton Failor - Geometry - 1906 - 440 pages
...triangles. 202 COROLLARY 2. Parallels comprehended between parallels are equal. PROPOSITION XXX. THEOREM 204 If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. HYPOTHESIS. ABCD is a quadrilateral, having AD = BC and AB = DC. CONCLUSION. ABCD is a parallelogram.... | |
 | Isaac Newton Failor - Geometry - 1906 - 431 pages
...triangles. 202 COROLLARY 2. Parallels comprehended between parallels are equal. PROPOSITION XXX. THEOREM 204 If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. HYPOTHESIS. ABCD is a quadrilateral, having AD = BC and AB = DC. CONCLUSION. ABCD is a parallelogram.... | |
 | International Correspondence Schools - Building - 1906 - 634 pages
...equal. SUGGESTION.— Show that in any rectangle A BCD the triangle ABC= triangle AB D. 3. Show that if the opposite sides of a quadrilateral are equal, the figure is a parallelogram. SUGGESTION.— Draw the diagonal. Then, by Art. 75, the triangles formed are equal. 4. Show that if... | |
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If the opposite sides of a quadrilateral are equal, the figure is a parallelogram. 
