In the figure 11.34, ABCD is a quadrilateral in which AB = AD
and BC = DC. Diagonals AC and BD intersect each other at o.
Show that
AABC = AADC
1) AAOB = AAOD
7) ACIBD
AC bisects BD
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Answer:1) Note that in △ABC and △ADC, we have AB=CD (given) AD=BC (given) AC=AC (common side)Thus it impplies that, △ABC≅△ADC (By SSS congruency)By CPCT, we get ∠DAC=∠BACor ∠DAO=∠BAO ....(1) (since AOC is a staright line)(2) Note that in △AOB and △AOD, we have AD=BC (given) AO=AO (common side) ∠DAO=∠BAO (from (1))Thus it impplies that, △AOB≅△AOD (By ASA congruency)(3) In previous part,we have proved that △AOB≅△AODThen by CPCT, we get ∠AOD=∠AOB ....(2)But these form linear pair, so we get ∠AOD+∠AOB=180°
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