1.

OC and OD are the bisectors of angle BCD and angle ADC respectively. If angle ADC=70° and angle BCD=60°, find the measures of angle DOC and angle ABC.

Answer»

Given: In the given figure, AB || CD and O is the MIDPOINT of AD. To prove: (i) ΔAOB ≅ ΔDOC. (ii) O is the midpoint of BC. Proof: (i) In ΔAOB and ΔDOC, ∠BAO = ∠CDO                    (Alternate interior angles, AB || CD) AO = DO                              (Given, O is the midpoint of AD) ∠AOB = ∠DOC                   (Vertically opposite angles)  ∴ By ASA congruence criteria, ΔAOB ≅ ΔDOC (ii) ∵ ΔAOB ≅ ΔDOC           [From (i)] ∴ BO = CO                           (CPCT) Hence, O is the midpoint of BC.Step-by-step explanation:



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