Thank you for visiting In quadrilateral ABCD diagonals AC and BD bisect one another Quadrilateral ABCD is shown with diagonals AC and BD intersecting at point P What statement. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Answer with explanation:
It is given that , quadrilateral A BC D, diagonals AC and B D bisect one another at point P.
In ΔAPB and ΔCPD
AP=PC
BP=PD
∠APB =∠CPD→Vertically opposite angles
ΔAPB ≅ ΔCPD→→[SAS]
→AB=CD⇒[CPCT]
→∠A BP=∠C DP⇒[C PCT]
Alternate interior angles are equal , so lines are parallel.
⇒AB║CD, and AB=CD
Similarly, we can prove ΔAPD ≅ ΔBPC, to prove AD║BC, and AD=BC.
⇒A Quadrilateral is a parallelogram , if one pair of opposite sides is equal and parallel.
Option C: The statement which is used to prove that quadrilateral ABCD is a parallelogram→→Triangles B PA and D PC are congruent.
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