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Standard IX

Mathematics

SAS Criteria for Congruency

In figure The...

Question

In figure The sides $B A$ and $C A$ have been produced such that $B A = A D$ and $C A = A E$ prove that segment $D E ∥ B C$

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Solution

In $Δ A B C$ and $Δ A D E$
$B A = A D$
$C A = A E$
$∠ B A C = ∠ E A D$ (vertically opposite angles)
$Δ A D A ≅ Δ B A C$ (SAS)
$E D | | B C$ (cpct)

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In the figure, the sides BA and CA have been produced such that BA = AD and CA = AE, Prove that segment DE || BC.

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In figure The sides BA and CA have been produced such that BA=AD and CA=AE prove that segment DE∥BC

In ΔABC and ΔADEBA=ADCA=AE∠BAC=∠EAD (vertically opposite angles)ΔADA≅ΔBAC (SAS)ED||BC (cpct)

In figure The sides $B A$ and $C A$ have been produced such that $B A = A D$ and $C A = A E$ prove that segment $D E ∥ B C$

In $Δ A B C$ and $Δ A D E$
$B A = A D$
$C A = A E$
$∠ B A C = ∠ E A D$ (vertically opposite angles)
$Δ A D A ≅ Δ B A C$ (SAS)
$E D | | B C$ (cpct)