Question

1 In the figure 10.22, 1 || m and p II and q 1 m. Show
that pll q. Give reasons for your answer.​

Answer 1

Given : L ||  M  

P ⊥ L

Q ⊥ M

To Find :  Show that p ll q

Solution:

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°)

∠PDC = 90°

=> ∠ADC = 90°               ( linear pair)

∠DAB = ∠PDC  = 90°   ( corresponding angles)  as L || M

∠DCB  + ∠ABC = 180° Interior angles are supplementary   as L || M

=> ∠DCB  + 90° = 180°

=> ∠DCB    = 90°

∠DCB =  ∠PDC = 90°  Alternate angles

hence p || q

QED

Also all the angles of ABCD are 90°

Hence ABCD is  a rectangle

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