If one side of a triangle is extended, then the exterior angle is equal to the two opposite interior angles and the three interior angles of a triangle are equal to two right angles.
Through a given point to draw a straight line parallel to a given straight line. Straight lines that are parallel to the same straight line are parallel If two straight lines are parallel, then a straight line that meets them makes the alternate angles equal, it makes the exterior angle equal to the opposite interior angle on the same side, and it makes the interior angles on the same side equal to two right angles. If a straight line that meets two straight lines makes an exterior angle equal to the opposite interior angle on the same side, or if it makes the interior angles on the same side equal to two right angles, then the two straight lines are parallel. If a straight line that meets two straight lines makes the alternate angles equal, then the two straight lines are parallel. If two triangles have two angles equal to two angles respectively, and one side equal to one side, which may be either the sides between the equal angles or the sides opposite one of them, then the remaining sides will equal the remaining sides (those that are opposite the equal angles), and the remaining angle will equal the remaining angle. On a given straight line and at a given point on it, to construct an angle equal to a given angle. To construct a triangle whose sides are equal to three given straight lines: thus any two of them taken together must be greater than the third. If one side of a triangle is extended, then the exterior angle is greater than either of the opposite interior angles.Īny two angles of a triangle are together less than two right angles.Ī greater side of a triangle is opposite a greater angle.Ī greater angle of a triangle is opposite a greater side.Īny two sides of a triangle are together greater than the third side When two straight lines intersect one another, the vertical angles are equal. If two straight lines are on opposite sides of a given straight line, and, meeting at one point of that line they make the adjacent angles equal to two right angles, then the two straight lines are in a straight line with one another. When a straight line that stands on another straight line makes two angles, either it makes two right angles, or it makes angles that together are equal to two right angles. To a given straight line that may be made as long as we please, and from a given point not on it, to draw a perpendicular line.
To draw a straight line at right angles to a given straight line from a given point on it. If two triangles have two sides equal to two sides respectively, and if the bases are also equal, then the angles will be equal that are contained by the two equal sides. If two angles of a triangle are equal, then the sides opposite them will be equal. In an isosceles triangle the angles at the base are equal. If two triangles have two sides equal to two sides respectively, and if the angles contained by those sides are also equal, then the remaining side will equal the remaining side, the triangles themselves will be equal areas, and the remaining angles will be equal, namely those that are opposite the equal sides. Given two unequal straight lines, to cut off from the longer lineĪ straight line equal to the shorter line.
On a given straight line to construct an equilateral triangle.įrom a given point to draw a straight line equal to a given straight line.
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