:
In geometry, two figures or objects are congruent if they have the same shape and size.

:
Each part: 1 Mark
In the given figure,
In$\mathrm{Δ}BCA$ and $\mathrm{Δ}BTA$,
BC = BT (Given)
CA = TA(Given)
BA = BA(Common side)
Thus, $\mathrm{Δ}BCAâ‰\dots \mathrm{Δ}BTA$ [By SSS congruence rule]
In $\mathrm{Δ}QRS$ and $\mathrm{Δ}TPQ$,
QT = QS(Given)
PQ = RS(Given)
PT = QR(Given)
Thus, $\mathrm{Δ}QRSâ‰\dots \mathrm{Δ}TPQ$ [By SSS congruence rule]

:
Definition: 1 Mark
Proof: 1Mark
If two angles have the same measurement, they are congruent. Also, if two angles are congruent, their measurementsare same.
We know thatin everyright-angled triangle, one angle is ${90}^{∘}$.
Example: Consider two right-angled triangles$\mathrm{Δ}AJU$ and $\mathrm{Δ}NIV$

In$\mathrm{Δ}AJU,\mathrm{âˆ}AJU={90}^{∘}$
and in $\mathrm{Δ}NIV,\mathrm{âˆ}NIV={90}^{∘}$
Since one angle is same in both, we can say that they have one pair of congruent angles.
So, if you take any two right-angled triangles, at least one pair of angles will be congruent, i.e. equal.

Answer: Option C. -> Both Statement 1 and statement 2 are true.
:
C

Two line segments are congruent only if they superimpose which is possible only if they have equal length and the converse is also true.
Hence, both the given statements are true.

Answer: Option B. -> $\angle C$ 
:
B

If two triangles are congruent, then their corresponding angles are equal.
Here, $\Delta$ ABC $\cong$ $\Delta$ RQP
$\therefore$ $\angle A$ =$\angle R$
$\angle B$ =$\angle Q$
$\angle P$ =$\angle C$
So, option B is correct.

Answer: Option C. -> ASA
:
C

Two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the corresponding angles and the side included between them, of the other triangle. This condition is called ASA congruence criterion.

Answer: Option A. -> SAS congruence condition
:
A

Two triangles are congruent if two sides and the angle included between them in one of the triangles are equal to the corresponding sides and the angle included between them of the other triangle. This condition is called SAS (Side, Angle included, Side) condition.
In the figure above,
AC = XZ
BC = YZ
$\mathrm{âˆ}ACB=\mathrm{âˆ}YZX$
$∴\mathrm{â–³}ACBâ‰\dots \mathrm{â–³}XZY$ by SAS criterion for congruency.

Answer: Option D. -> RHS congruence condition
:
D

Two right-angled triangles are congruent if the hypotenuse and the leg of one of the triangles are equal to the hypotenuse and the corresponding leg of the other triangle. This condition is called RHS congruence of two triangles and is applicable only to right angled triangles.

Answer: Option C. -> $\Delta ABC\cong \Delta FED$​
:
C

In  $\mathrm{Δ}ABC\text{Â}and\text{Â}\mathrm{Δ}FED$

BC = ED  (Given in the figure);
$\mathrm{âˆ}$ B = $\mathrm{âˆ}$ E = ${90}^{∘}$
$\mathrm{âˆ}$ A = $\mathrm{âˆ}$ F   (Given in the figure)
$⇒$ $\mathrm{âˆ}$C = $\mathrm{âˆ}$D  (Angle sum property of triangle)

Therefore, by ASA congruence condition, $\mathrm{Δ}ABCâ‰\dots \mathrm{Δ}FED$ .

Answer: Option B. -> SSS
:
B

When three sides of a triangle are equal to corresponding three sides of another triangle, the triangles are congruent by Side-Side-Side (SSS) congruence.

In the above figure,
AB = PQ
AC = PR
BC = QR
Since the sides of $\mathrm{â–³}ABC$ are equal to corresponding sides of $\mathrm{â–³}PQR$, $\mathrm{â–³}ABCâ‰\dots \mathrm{â–³}PQR$ by SSS criterion for congruency.