Question

" If Learning Task 5 : In your answer sheet , prove the theorem , using the given below . quadrilateral is inscribed in a circle , then supplementary . " its opposite angles are Given : Quadriateral ABCD is inscribed in OE Prove : ABC and are supplementary DCB and are supplementary C B

Answer 1

Answer:

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Answer 2

Learning Task 5

Given : Quadriateral ABCD is inscribed in the circle

Prove : ∠ABC and ∠DCB are supplementary

∠ADC = 1/2 arc ABC      ( the measure of inscribed angle is half the measure  of intercepted arc)

∠ABC = 1/2 arc ADC

∠BAD = 1/2 arc BCD

∠BCD = 1/2 arc BAD

arc ABC + arc ADC = 360°   (arc addition postulate)

arc BAD + arc BCD = 360°

1/2 (arc ABC + arc ADC = 360°)     (multiplication property of equality)

1/2 (arc BAD + arc BCD = 360°)

1/2 (arc ABC + arc ADC) = 180°    

1/2 (arc BAD + arc BCD) = 180°

∠ADC + ∠ABC = 180°

∠BCD + ∠BAD = 180°

Hence, proved that ∠ABC and ∠DCB are supplementary