If two right-angled triangles have their hypotenuses equal, and one side of the one equal to one side of the other, the triangles are congruent. If two sides of a triangle are unequal, the greater side has the greater angle opposite to it ; and the converse.... Calendar - Page 216by University of Allahabad - 1908Full view - About this book
| Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...only one perpendicular can be drawn to that line. THEOR. 19. Of all the straight lines that can be **drawn to a given straight line from a given point outside it, the perpendicular is the shortest** ; and of the others, those which make equal angles with the perpendicular are equal ; and that which... | |
| James Maurice Wilson - 1878 - 450 pages
...therefore ab = cd. QED Similarly the converse propositions may be proved. THEOREM 32. If there are three **parallel straight lines, and the intercepts made by...any straight line that cuts them are equal, then the** intercepts on any other straight line that cuts them are equal. Let the three parallel straight lines... | |
| Education, Higher - 1881 - 504 pages
...the angles in a regular pentagon, decagon, and dodecagon. 2. Of all the straight lines that can be **drawn to a given straight line from a given point outside it, the perpendicular is the shortest** ; and of the others, those which make equal angles with the perpendicular are equal ; and that which... | |
| Mathematical association - 1883 - 86 pages
...sides of the triangle, but contain a greater angle. THEOR. 15. Of all the straight lines that can be **drawn to a given straight line from a given point outside it, the perpendicular is the shortest;** and of the others, those which make equal angles with the perpendicular are equal; and that which makes... | |
| Mathematical association - 1884 - 146 pages
...and OC is less than the perimeter of the triangle. THEOR. 15. Of all the strain-lit lines that can be **drawn to a given straight line from a given point outside it, the perpendicular is the shortest** ; and of the others, those which make equal angles with the perpendicular are equal ; and that which... | |
| Lewis Carroll - Geometry - 1885 - 318 pages
...are equal, both being zero, whether the Lines are equal or not. P. 1 8, Th. 33. ' If there are three **parallel straight Lines, and the intercepts made by...on any straight Line that cuts them are equal, then** etc.' The subject of this Proposition is inconceivable : there are three intercepts, and by no possibility... | |
| Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...=».FH. Hence AC : EG : : BD : FH. Def. 5. QED COR. i. If there are three parallel straight lines, **the intercepts made by them on any straight line that cuts them are** to one another in the same ratio as the corresponding intercepts on any other straight line that cuts... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...Prop. 6, and is an immediate inference from Prop. 5. Ex. 24. — Of all straight lines that can be **drawn to a given straight line from a given point outside it, the perpendicular is the shortest** ; and of the others those which make equal angles with the perpendicular are equal; and that which... | |
| Education - 1903 - 692 pages
...can be drawn to a given straight "* 'rom a given point outside it, the perpendicular is the "hottest. **The opposite sides and angles of a parallelogram are...the corresponding intercepts on any other straight** line that cuts them are also equal. Areas. — Parallellograms on the same or equal bases and of the... | |
| Association for the Improvement of Geometrical Teaching - 1903 - 342 pages
...and OC is less than the perimeter of the triangle. THEOE. 15. Of all the straight lines that can be **drawn to a given straight line from a given point outside it, the perpendicular is the shortest** ; and of the others, those which make equal angles with the perpendicular are equal ; and that which... | |
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