diagonal ac. of a quadrilateral ABCD bisect the angles A and C. prove that AB = AD and CB = CD {please don't spam and it is urgent please solve fast}
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Answer:
Since diagonal AC bisects the angles ∠A and ∠C,
we have ∠BAC=∠DAC and ∠BCA=∠DCA.
In triangles ABC and ADC,
we have
∠BAC=∠DAC (given);
∠BCA=∠DCA (given);
AC = AC (common side).
So, by ASA postulate, we have
△BAC≅△DAC
⇒ BA = AD and CB = CD (Corresponding parts of congruent triangle).
solution
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Answer:
Answer
Since diagonal AC bisects the angles ∠A and ∠C,
we have ∠BAC=∠DAC and ∠BCA=∠DCA.
In triangles ABC and ADC,
we have
∠BAC=∠DAC (given);
∠BCA=∠DCA (given);
AC = AC (common side).
So, by ASA postulate, we have
△BAC≅△DAC
⇒ BA = AD and CB = CD (Corresponding parts of congruent triangle).
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