1. In the figure 10.22, 1 || m and plland q 1 m. Show
that p ll q. Give reasons for your answer.
2. What can you say about the quadrilateral ABCD
given in figure 10.22? Is it a rectangle? Justify your
Answers
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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Answer:
p||q
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