CBSE Class 9 Answered

Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other.

Asked by SIDDHARTH SHARMA | 13 Sep, 2014, 11:50: PM

Expert Answer

C o n s i d e r space t h e space f o l l o w i n g space f i g u r e.

L e t space w space a n d space x space a r e space t w o space i n t e r s e c t i n g space l i n e s. L e t space y space b e space a space l i n e space p e r p e n d i c u l a r space t o space w space a n d space z space b e space a space l i n e space p e r p e n d i c u l a r space t o space x. rightwards double arrow y perpendicular w space a n d space z perpendicular x W e space n e e d space t o space p r o v e space t h a t space y space a n d space z space a r e space i n t e r s e c t i n g space l i n e s. L e t space u s space p r o v e space t h i s space b y space t h e space m e t h o d space o f space c o n t r a d i c t i o n. A s s u m e space t h a t space y space a n d space z space d o space n o t space i n t e r s e c t space e a c h space o t h e r. rightwards double arrow y space a n d space z space a r e space p a r a l l e l rightwards double arrow y parallel to z A n d space y parallel to z space a n d space z perpendicular x rightwards double arrow y perpendicular x..... left parenthesis 1 right parenthesis A l s o comma space w e space h a v e comma space y perpendicular w space left parenthesis g i v e n right parenthesis... left parenthesis 2 right parenthesis F r o m space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma space w parallel to x space a n d space t h i s space i s space c o n t r a d i c t i n g space t h e space f a c t space t h a t space w space a n d space x a r e space i n t e r s e c t i n g space l i n e s. H e n c e space o u r space a s s u m p t i o n space t h a t space y space a n d space z space a r e space p a r a l l e l space i s space w r o n g. space T h e r e f o r e comma space t h e space l i n e s space y space a n d space z space a r e space i n t e r s e c t i n g space e a c h space o t h e r. space

Answered by Vimala Ramamurthy | 14 Sep, 2014, 10:47: AM

CBSE Class 9 Answered

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CBSE Class 9 Answered

Concept Videos

Transversals, interior and exterior angles made by them ...

Parallel Lines and Transversals ...

Quick revision and problem-solving on Transversals ...

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