In the figure, chord EG congruent chord FH. prove that quadrilateral EFHG is a trapezium
(Hint : use the inscribed angel theorem)
Answers
Given : chord EG congruent chord FH.
To Find : prove that quadrilateral EFHG is a trapezium
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°)
chord EG congruent chord FH.
Equal chords subtends equal angle
=> ∠EFG = ∠HGF
∠EFG and ∠HGF are alternate interior angles
as alternate interior angles hence lines will be parallel
=> EF || GH
Hence EFGH is trapezium
QED
Hence Proved
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