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Q15. In a quadrilatea quadrilateral ABCD ZA+ZD = 180° Does this mean AB | DC? Why? What special namedoes this quadrilateral have? |
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Answer» Since, ABCD is a quadrilateral and ∠A+∠D= 180°. From the figure, we can see that ∠A and ∠D form the adjacent angle pair and it is already known that the two adjacent angles always add to give their angle sum equal to 180°. Also, adjacent angles are formed if the two lines are parallel which means that if two adjacent angles are given then the two ,lines must be parallel, therefore AB is parallel to CD. If the two lines are parallel and also, the angle sum of two adjacent angles equal to 180°, then this type of quadrilateral is known as "Trapezium". 4 is the correct answer Yes. If Angle A + Angle D = 180°,then definitely AB || DC.With this information, we can conclude that only one pair of opposite sides are parallel. Hence, a special name for this quadrilateral will be trapezium.See picture for the proof. |
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