Question

जर एखादी रेषा एका प्रतलातील दोन समांतर रेषापैकी एका रेषेला लंब असेल तर ती दुसऱ्या रेषेलाही लंब असते, हे सिद्ध करा.​

Answer 1

Given :  a line is perpendicular to one of the two parallel lines in a plane

To Find : Prove that line is also perpendicular to the other line.

Solution :

Let say line AB || CD

and transversal  line intersects AB and  CD  at  PQ

and PQ ⊥  AB

∠APQ = ∠BPQ = 90°

Properties of angles formed by transversal line  with two parallel lines :

• Corresponding angles are congruent.  

• Alternate angles are congruent.  ( Interiors & Exterior  both )  

• Interior angles are supplementary. ( adds up to 180°)

Alternate angles are congruent.

Hence ∠CQP =  ∠BPQ   = 90°  

and   ∠DQP =  ∠APQ   = 90°  

Hence  PQ ⊥ CD  also

QED

Hence proved

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