In the given figure,PQ || RS || TU,PQ=5cm,TU=7.5cm,RU=a and RS=b

T.P:incrementUTR ~incrementPQR and then solve for a and b

Asked by hrmeenal24 | 14th Feb, 2020, 06:50: AM

Expert Answer:

In the given figure, PQ || RS || TU
To prove tha triangles UTR and PQR are similar
I n space triangle P Q R space a n d space triangle U T R comma
angle P R Q equals angle U R T space... space left parenthesis V e r t i c a l l y space o p p o s i t e space a n g l e s right parenthesis
angle P Q R equals angle U T R space... space left parenthesis A l t e r n a t e space a n g l e s space a s space P Q space vertical line vertical line space T U space a n d space Q T space i s space t h e space t r a n s v e r s a l right parenthesis
therefore space triangle P Q R space tilde space triangle U T R space... space left parenthesis U sin g space A A space s i m i l a r i t y space t e s t right parenthesis
T h e r e f o r e comma space u sin g space t h e space p r o p e r t y space o f space s i m i l a r space t r i a n g l e s
space i. e. space r a t i o space o f space t h e space c o r r e s p o n d i n g space s i d e s space o f space t w o space s i m i l a r space t r i a n g l e s space a r e space s a m e
rightwards double arrow fraction numerator P Q over denominator U T end fraction equals fraction numerator Q R over denominator T R end fraction equals fraction numerator P R over denominator U R end fraction

rightwards double arrow fraction numerator 5 over denominator 7.5 end fraction equals fraction numerator P R over denominator a end fraction
rightwards double arrow a equals 1.5 P R

Answered by Renu Varma | 14th Feb, 2020, 11:09: AM