CalendarUniversity of Allahabad, 1908 |
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Page 162
... one equal to two angles of the other , each to each , and also one side of the one equal to the corresponding side of the other , the triangles are congruent . If two sides of a triangle are equal , the angles oppo- site to these sides ...
... one equal to two angles of the other , each to each , and also one side of the one equal to the corresponding side of the other , the triangles are congruent . If two sides of a triangle are equal , the angles oppo- site to these sides ...
Page 216
... one equal to two angles of the other , each to each , and also one side of the one equal to the corresponding side of the other , the triangles are congruent . If two sides of a triangle are equal , the angles opposite to these sides ...
... one equal to two angles of the other , each to each , and also one side of the one equal to the corresponding side of the other , the triangles are congruent . If two sides of a triangle are equal , the angles opposite to these sides ...
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Popular passages
Page 218 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Page 216 - If two triangles have two sides of the one equal to two sides of the other, each to each, and also the angles contained by these sides equal, the triangles are congruent.
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Page 216 - 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. 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.
Page 165 - If a straight line is drawn parallel to one side of a triangle, the other two sides are divided proportionally ; and the converse. If two triangles are equiangular their corresponding sides are proportional ; and the converse. If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar. The...
Page 162 - When a straight line cuts two other straight lines, if (i) a pair of alternate angles are equal, or (ii) a pair of corresponding angles are equal, or (iii) a pair of interior angles on the same side of the cutting line are together equal to two right angles, then the two straight lines are parallel ; and the converse.
Page 163 - If there are three or more parallel straight lines, and the intercepts made by them on any straight line that cuts them are equal, then the corresponding intercepts on any other straight line that cuts them are also equal.
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Page 162 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
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