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Standard VII

Mathematics

SAS Criteria for Congruency

In the figure...

Question

In the figure below, the diagonal $A C$ of quadrilateral $A B C D$ bisects $∠ B A D$ and $∠ B C D .$ Then $B C = m D C$ .Find $m$

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Solution

Given:- $∴$ $∠ D A C = ∠ B A C$
$∠ A C D = ∠ A C B$
To prove $∴$ $B C = B D$
proof therefore In triangle ABC and triangle ADC
$∠ B A C = ∠ D A C$
$∠ A C B = ∠ A C D$
$A C = A C$
so, $Δ A B C ≅ Δ A D C$
$\Rightarrow B C = D C$

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In the figure below, the diagonal AC of quadrilateral ABCD bisects ∠BAD and ∠BCD. Then BC=mDC.Find m

Given:- ∴ ∠DAC=∠BAC∠ACD=∠ACBTo prove∴ BC=BDproof therefore In triangle ABC and triangle ADC∠BAC=∠DAC∠ACB=∠ACDAC=ACso, ΔABC≅ΔADC⇒BC=DC

In the figure below, the diagonal $A C$ of quadrilateral $A B C D$ bisects $∠ B A D$ and $∠ B C D .$ Then $B C = m D C$ .Find $m$

Given:- $∴$ $∠ D A C = ∠ B A C$
$∠ A C D = ∠ A C B$
To prove $∴$ $B C = B D$
proof therefore In triangle ABC and triangle ADC
$∠ B A C = ∠ D A C$
$∠ A C B = ∠ A C D$
$A C = A C$
so, $Δ A B C ≅ Δ A D C$
$\Rightarrow B C = D C$