How many criterion of congruency of triangles are there?

$\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ is a parallelogram and $\mathrm{A}\mathrm{P}$ and $\mathrm{C}\mathrm{Q}$ are perpendiculars from vertices $\mathrm{A}$ and $\mathrm{C}$ on diagonal $\mathrm{B}\mathrm{D}$. Show that $\mathrm{\Delta }\mathrm{A}\mathrm{P}\mathrm{B}\cong \mathrm{\Delta }\mathrm{C}\mathrm{Q}\mathrm{D}$.

In parallelogram $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D},$ two points $\mathrm{P}$ and $\mathrm{Q}$ are taken on diagonal $\mathrm{B}\mathrm{D}$ such that $\mathrm{D}\mathrm{P}=\mathrm{B}\mathrm{Q}$. Show that $\mathrm{\Delta }\mathrm{A}\mathrm{P}\mathrm{D}\cong \mathrm{\Delta }\mathrm{C}\mathrm{Q}\mathrm{B}$.

In $∆\mathrm{ABC}, \mathrm{D}$ is the midpoint of $\mathrm{BC}$. If $\mathrm{DL}\perp \mathrm{AB}$ and $\mathrm{DM}\perp \mathrm{AC}$ such that $\mathrm{DL}=\mathrm{DM}$, prove that $\mathrm{AB}=\mathrm{AC}$.

Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.

From the information shown in the figure, in ΔABC and ΔPQR

 
∠ABC ≅ ∠PQR

 
seg BC ≅ seg QR

 
∠ABC = ∠PRQ

 
∴ ΔABC ≅ ΔPQR ……………………____ test

 
∴ ∠BAC = _____……………………corresponding angles of congruent triangles.

 
seg AB ≅ ____………………….. corresponding sides of congruent triangles.

 
____ = seg PR …………………corresponding side of congruent triangles.

In the given figure, $\mathrm{ABCD}$ is a square and $\mathrm{P}$ is a point inside it such that $\mathrm{PB}=\mathrm{PD}$. Prove that $\mathrm{CPA}$ is a straight line.