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Draw and prove that opposite angles of a paralelogram are equal |
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Answer» Here, ABCD is a parallelogram with AC as its diagonal.We know, in parallelogram opposites sides are parallel.So, AB∥DC and AD∥BCSince, AB∥DC and AC is the transversal⇒ ∠BAC=∠DCA ---- ( 1 ) [ Alternate angles ]Similarly, AD∥BC and AC is the transversal.⇒ ∠DAC=∠BCA ---- ( 2 ) [ Alternate angles ]ADDING ( 1 ) and ( 2 ),⇒ ∠BAC+∠DAC=∠DCA+∠BCA⇒ ∠BAD=∠DCBSimilarly, we can prove, ∠ADC=∠ABC∴ We have proved that, OPPOSITE angles of a parallelogram are equal.solution |
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