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In the Below Fig, Arms Ba and Bc of `∠`Abc Are Respectively Parallel to Arms Ed and Ef of `∠`Def. Prove that `∠`Abc = ∠Def. - Mathematics

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In the below fig, arms BA and BC of `∠`ABC are respectively parallel to arms ED and EF of
`∠`DEF. Prove that `∠`ABC = ∠DEF.

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Solution

Given AB || DE and BC ||lry  EF

To prove: `∠`ABC = `∠`DEF

Construction: Produce BC to x such that it intersects DE at M.

Proof: Since AB || DE and BX is the transversal

∴`∠`ABC = `∠`DMX         [Corresponding angles]           ……..(ii)

Also,

BX || EF and DE is the transversal

∴`∠`DMX = `∠`DEF     [Corresponding angles]           ……..(ii)

From (i) and (ii)

∴ABC = `∠`DEF

 

 

Concept: Parallel Lines and a Transversal
  Is there an error in this question or solution?

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Exercise 10.4 | Q 26 | Page 49

Video TutorialsVIEW ALL [1]

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