Text book of Elementary Plane Geometry

Cover Text book of Elementary Plane Geometry
Text book of Elementary Plane Geometry
Julius Petersen
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The distance between two parallels is a; any line AB is drawn between the parallels, and the two supplement- ary angles A and B are bisected; how great is the alti- tude of the right-angled triangle, formed thereby?
65. In a right-angled triangle, the right angle is bisected, from the point where the bisecting line cuts the hypothenuse, lines are drawn parallel to the two sides containing the right angle. Prove that the figure contained by these two lines and the two sides is a square.
66. The
...point C bisects the line AB. The three points are projected on to any line in A^ B l and C l ' shew that C l bisects A l B l .
67. Two points A and B lie on the same side of a straight line. From A a line is drawn to the point 0, which lies symmetrically with B. This line cuts the given line in a point D. Prove that AD and ED make equal angles with the given line.
68. A line is parallel to the diagonal of a parallelogram; shew that the one pair of opposite sides cut off a part of the line, equal to the part cut off by the other pair.


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