Question

in the given figure if ab= cd and ad=bc, then prove that triangle adc = cba​

Answer 1

Given :-

• AD = BC

• AB = CD

To Prove :-

• ∆ ADC ≅ ∆ CBA

Concept Used :-

• Congruency of triangles.

Proof :-

$\bf :\longmapsto\:In \: \triangle \: ADC \: and \: \triangle \: CBA$

$\rm :\longmapsto\:AD = BC \: \: \: \: \: \: \: \: \: \: \{given \}$

$\rm :\longmapsto \: AB = CD \: \: \: \: \: \: \: \: \: \: \{given \}$

$\rm :\longmapsto \: AC = AC \: \: \: \: \: \: \: \: \: \: \{common \}$

$\bf\implies \:\triangle \: ADC \: \cong \: \triangle \: CBA \: \: \{SSS \: Congruecy \}$

$\large{\boxed{\boxed{\bf{Hence, Proved}}}}$

Additional Information :-

There are 5 types of Congruency in triangles :-

$\rm :\longmapsto\:SSS \: Cogruency \: Rule$

$\rm :\longmapsto\:SAS \: Cogruency \: Rule$

$\rm :\longmapsto\:AAS \: Cogruency \: Rule$

$\rm :\longmapsto\:ASA \: Cogruency \: Rule$

$\rm :\longmapsto\:RHS \: Cogruency \: Rule$

Note :-

• There is no AAA Congruency Rule