Question

State the condition by which the following pairs of triangles are congruent.

Answer 1

1) AB = AD
BC = CD
and AC = CA
Therefore by SSS condition, $△ABC\cong △ADC$.

2) AC = BD
AD = BC and AB = BA
Therefore by SSS condition, $△ABD\cong △BAC$.

3) AB = AD
$\angle BAC=\angle DAC$
and AC = AC
Therefore by SAS condition, $△BAC\cong △DAC$.

4) AD = BC
$\angle$ DAC = $\angle$BCA
and AC = CA
Therefore by SAS condition, $△ABC\cong △ADC$.