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 legof the other triangle. This condition is called RHS congruence of two trianglesand is applicable only to right angled triangles.

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. -> True
:
A
For two angles to be congruent, they should coincidewhen superimposed. This is only possible if both the angles are equal. Hence, the given statement is true.

Answer: Option B. -> False
:
B
If all the corresponding angles of twotriangles are equal, then triangles will havethe same shape, but not necessarily the same size and hence may not be congruent. See the figure below. The corresponding angles of both triangles are equal, but still their sizes are not same and hence they are not congruent.

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 themof the other triangle. This condition is called SAS (Side, Angle included, Side)condition.
In the figure above,
AC = XZ
BC = YZ
$\angle ACB=\angle YZX$
$\therefore △ACB\cong △XZY$ by SAS criterion for congruency.

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 $△ABC$ are equal to corresponding sides of $△PQR$, $△ABC\cong △PQR$ by SSS criterion for congruency.

Answer: Option B. -> ∠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 Bis correct.

Answer: Option A. -> SSS, SAS, ASA, AAS, RHS
:
A
Criteria for congruence of triangles are SSS, SAS, ASA, AAS, RHS.
SSS- Two triangles are congruent if all the 3 corresponding sides of the given triangles are equal.
SAS- Two triangles are congruent if 2 corresponding sides of the given triangles and the corresponding anglebetween those sides are equal to each other.
ASA-Two triangles are congruent if two angles and the included side of one triangle are equal to the corresponding angles and sides of other triangles.
AAS-Two triangles are congruent iftwo pairs of corresponding angles and a pair of opposite sides are equal.
RHS-If the hypotenuse and a side of a right angled triangle are congruent with the hypotenuse and the corresponding side
of the other right angled triangle, then the two triangles are congruent with each other.

Answer: Option A. -> x = 15, y = 9 
:
A
Given, $AB=AC$
$⟹94=6x+4⟹6x=90⟹x=15$

In $△ABD$ and $△ACD$,
(i) $\angle ADB=\angle ADC={90}^{\circ }$ ... (given)
(ii) AB = AC ...(given)
(iii) AD = AD ... (common side)
$\Rightarrow$$△ABD\cong △ADC$ ... (RHS congruence rule)
Then, $BD=CD$ ...(CPCT)
$\Rightarrow 2y–7=11\Rightarrow 2y=18\Rightarrow y=9$

Answer: Option B. -> x=48∘,y=56∘
:
B
Consider $△ABC$ and $△ADC$

(i) AB = CD ...... (given)
(ii) BC = DA...... (given)
(iii) AC = AC ...... (common)
$\therefore △ABC\cong △CDA$ ... (SSS Postulate)
$\Rightarrow \angle ABC=\angle CDA$ ..... (CPCT)
$\therefore x={48}^{\circ }$
$\Rightarrow \angle BCA=\angle DAC$ ......(CPCT)
$\therefore y={56}^{\circ }$