Ex 3.3, 10 Explain how this figure is a trapezium. Which of its two sides are parallel? Given: A quadrilateral KLMN having
∠L = 80°
and ∠M = 100°
To Prove: KLMN is a trapezium.
i.e. KL ∥ NM
Construction: Extend LM to O.
Proof:
For Line Segments NM and KL,
with MO is a transversal .
∠ M + ∠ L = 180°
Thus,
Sum of Interior angles on same side of transversal is 180°
Which is only possible if NM and KL are parallel lines
Therefore, NM ∥ KL
Since, KLMN is quadrilateral with KL ∥ NM
∴ KLMN is a trapezium

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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