Free Congruence of Triangles 02 Practice Test - 7th grade 

In the given figure:

In  $\Delta ABCand\Delta PQR$

AB = PR

BC = PQ

AC = QR

Therefore, $\Delta ABC\cong \Delta RPQ$ by SSS criterion.

Since all congruent triangles are similar triangles. $\Delta ABCand\Delta RPQ$  are also similar.

In the given figure:

In  $\Delta ABCand\Delta PQR$

AB = PR

BC = PQ

AC = QR

Therefore, $\Delta ABC\cong \Delta PQR$ by SSS criterion.
Hence, the statement is false.

In the given figure:

In  $\Delta ABCand\Delta PQR$

AB = PR = 5 cm

BC = PQ

AC = QR = 7 cm

Therefore, $\Delta ABC\cong \Delta PQR$ by SSS criterion.

Since perimeter = 18cm

$\Rightarrow$ AB + AC + BC = 18 cm,

$\Rightarrow$ BC = 18 - 5 - 7 = 6 cm.

Therefore, 
AB = PR = 5 cm

BC = PQ = 6 cm

AC = QR = 7 cm 
So, the answer is 7 cm.

In the given figure:

In  $\Delta ABCand\Delta PQR$

AB = PR (Given)

BC = PQ (Given)

AC = QR (Given)

Therefore, $\Delta ABC\cong \Delta PQR$ by SSS condition.

Therefore,

$\angle A=\angle R={50}^{\circ }$;

$\angle B=\angle P$;

$\angle C=\angle Q={60}^{\circ }$.

Using angle sum property in  $\Delta$ ABC,
$\angle A+\angle B+\angle C={180}^{\circ }$
$\Rightarrow$   ${50}^{\circ }+\angle B+{60}^{\circ }={180}^{\circ }$
$\Rightarrow$  $\angle B={70}^{\circ }$

In $\Delta ABD\text{and}\Delta BAC$,
AD = BC  (Given)
$\angle BAD$ = $\angle CBA$ (Given)
AB = BA  (Side common to both triangles)
Hence $\Delta ABD\cong \Delta BAC$
(by SAS congruence condition). 
Thus, $\angle ABD$ = $\angle BAC$
(congruent parts of congruent triangles). 

We know that if two triangles are congruent, then their corresponding parts are equal.

Since $\Delta DEF\cong \Delta BCA$, therefore $\angle E=\angle C$ and $FD=AB$.

In $\Delta ABCand\Delta PQR$​

AB = PQ = 4cm ,  (Given)

BC = QR = 5 cm,  (Given) 

AC = PR = 6 cm;  (Given)

Hence, $\Delta ABC\cong \Delta PQR$  (By SSS criterion).

Since  $\Delta ABC\cong \Delta PQR$,
corresponding sides of congruent triangles will be equal.
Hence, AB = PQ.

The criteria for congruence of triangles are SSS criterion, SAS criterion, ASA criterion and RHS criterion.

AAA is not a criterion for congruence as it does not ensure the equality of sides of the two triangles.

Note: AAA is a criterion for 'Similarity' of triangles.

Two triangles(or any geometric figures) are congruent if they have same shape and equal measures (i.e., all corresponding sides and angles are equal). This is because two triangles are said to be congruent only if they coincide when superimposed which is possible only if all their corresponding angles and sides are equal.