In the given figure, prove that AB || CD. [3]
Answers
because corresponding angle are equal
Given : A figure showing few lines
To Find : prove that AB || CD
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°)
AE is transversal for AB & EF
130° + 50° = 180° Interior angles are supplementary
=> AB ║ EF
30° + 50° = 80°
CE is transversal for CD & EF
80° = 80°
Alternate Interiors angles are congruent.
Hence CD || EF
AB ║ EF
CD || EF
=> AB || CD
Hence Proved
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