Q10 of 16 Page 88

Each pair of arms of two angles is parallel to each other. Let’s prove either these angles are equal in measurement or they are supplementary.


Given that BC||DE.


∠ABC+∠CBD=180° (straight angle)


⇒ ∠ABC=180°-∠CBD ……………….(1)


Also, draw FG||BD,


∴ BFGD is a parallelogram


So, ∠CBD+∠BDE=180° (co-interior angles)


⇒ ∠BDE =180°-∠CBD ……………….(2)


From (1) and (2)


⇒ ∠ABC=∠BDE


Hence Proved.


More from this chapter

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8

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 9

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The diagonal AC of the parallelogram ABCD bisects ∠BAD. Let’s prove that the diagonal AC also bisects ∠BCD.

 12

Let’s prove if one angle of a parallelogram is right angle, then all other angles of the parallelogram are also right angles.