Q. 65.0( 2 Votes )

# ΔABC and ΔDEF are two triangles such that AB, BC are respectively equal and parallel to DE, EF; show that AC is equal and parallel to DF.

Answer :

In the ΔABC and ΔDEF,

AB = DE and AB ïï DE

BC = EF and BC ïï EF

To Prove: AC = DF and AC ïï DF

Construction: Join AD, CF and BE

Proof: Since AB = DE and AB ïï DE

.

.

Similarly quadrilateral BEFC is a parallelogram

.

From (i) and (ii) we get,

AD = CF and AD ïï CF

.

.

AB = DE and AB ïï DE

BC = EF and BC ïï EF

To Prove: AC = DF and AC ïï DF

Construction: Join AD, CF and BE

Proof: Since AB = DE and AB ïï DE

.

^{.}. Quadrilateral ABED is a parallelogram (one pair of opposite sides are equal and parallel).

^{.}. AD = BE and AD ïï BE .....(i)Similarly quadrilateral BEFC is a parallelogram

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^{.}. BE = CF and BE ïï CF......(ii)From (i) and (ii) we get,

AD = CF and AD ïï CF

.

^{.}. ADFC is a parallelogram.

^{.}. AC = DF and AC ïï DFRate this question :

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