How to prove this statement- "If in a quadrilateral only one pair of opposite angles are known to be equal then,prove that it is not necessarily a parallelogram."?
2026-03-27 02:33:09.1774578789
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How shall I prove the given statement?
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Construct two lines, that are not parallel nor perpendicular to each other. At some point far away from the intersection point, construct a perpendicular to one line that will intersect the other. At a another point on the second line, construct a perpendicular from the second line that intersects the first.
The resulting figure is a quadrilateral. It is not a parallelogram. And two of its opposite angles are right angles.
Draw a diameter of a circle, then draw an incribed angle from the endpoints into each semicircle. These are equal (both right angles), but the angles created at the ends of the diameter are not necessarily equal, therefore the quadrilateral need not be a parallelogram.
For general angles on either side of the quadrilateral, choose the initial two points, draw a suitable arc of a circle for the angle required on one side and then reflect it across the line joining the first two points to make a construction circle for the other side.