State true or false:
Two straight lines are perpendicular to the same third line; then they are parallel to each other also.

True

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False

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Solution

The correct option is A True
$G i v e n C D ⊥ A B s o ∠ A C D = ∠ D C B = 90^{o} A l s o g i v e n F E ⊥ A B s o ∠ F E A = ∠ F E B = 90^{o} N o w ∠ A C D = ∠ F E A (C o r r e s p o n d i n g a n g l e s i f C D ∥ E F & A B i s t h e t r a n s v e r s a l .) H e n c e t w o s t r a i g h t l i n e s t h a t a r e p e r p e n d i c u l a r t o t h e s a m e t h i r d l i n e, a r e p a r a l l e l t o e a c h o t h e r .$

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Similar questions

State true or false:

Two lines perpendicular to another line are perpendicular to each other as well.

If two straight lines are perpendicular to the same line, prove that they are parallel to each other.

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