Q11 of 16 Page 88

The diagonal AC of the parallelogram ABCD bisects ∠BAD. Let’s prove that the diagonal AC also bisects ∠BCD.


Given ABCD is a parallelogram with diagonals AC and BD.


Also, AC bisects ∠BAD


So, ∠DAC=∠BAC …………..(1)


Since, CD||AB,


∠DCA=∠BAC (alternate interior angles)


And ∠BCA=∠DAC (alternate interior angles)


From (1),


∠DAC=∠BAC


⇒ ∠BCA=∠DCA


Hence, AC bisects ∠BCD


More from this chapter

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