In the given figure, $∆\mathrm{ABC}$ and $∆\mathrm{ABD}$ are triangles on the same base $\mathrm{AB}$. $\mathrm{AC}=\mathrm{BD}$ and $\mathrm{BC}=\mathrm{AD}$.

Which of the following statements is true/false.

$∆\mathrm{ABC}\cong ∆\mathrm{ADB}$

There are two congruent triangles in the figure. Sort them out and write in symbolic language.

In the adjacent figure, $\mathrm{AB}=\mathrm{AC}$ and $\angle \mathrm{DAB}=\angle \mathrm{CAD}$ are $∆\mathrm{ABD}$ and $∆\mathrm{ADC}$ congruent? if yes why $?$

Which of the following triangles is similar to which triangle in all aspects?

$AD$ is the bisector of $\angle A$ in the figure and $AD\perp BC$.

Is $△ADB\cong △ADC?$

$AD$ is the bisector of $\angle A$ in the figure and $AD\perp BC$.

Is it correct to say $BD=DC?$

Line $AX$, bisects the angles $\angle CAB \text{and} \angle BDC$ in the figure. Describe the three facts which proves that $△ABD\cong △ACD$.

Construct a right-angled triangle $△ABC$, in which hypotenuse $AC=7 cm, \angle B=90° \& AB=4 cm$, construct another triangle $△XYZ$, in which hypotenuse $XZ=7 cm$, $ZY= 4 cm \& \angle Y=90°$. Prove the congruence of these triangles.