# Free Congruence of Triangles 02 Practice Test - 7th grade

### Question 1

Consider the figure below:

The triangles ABC and PQR are similar.

True

False

#### SOLUTION

Solution :A

In the given figure:

In ΔABC and ΔPQR

AB = PR

BC = PQ

AC = QR

Therefore, ΔABC≅ΔRPQ by SSS criterion.

Since all congruent triangles are similar triangles. ΔABC and ΔRPQ are also similar.

### Question 2

Consider the figure below:

The two triangles are congruent by SAS criterion only.

True

False

#### SOLUTION

Solution :B

In the given figure:

In ΔABC and ΔPQR

AB = PR

BC = PQ

AC = QR

Therefore, ΔABC≅ΔPQR by SSS criterion.

Hence, the statement is false.

### Question 3

Consider the figure below:

If AB = 5 cm; QR = 7cm; then find the value of AC (in cm.), if the perimeter of △ABC is 18cm.

#### SOLUTION

Solution :In the given figure:

In ΔABC and ΔPQR

AB = PR = 5 cm

BC = PQ

AC = QR = 7 cm

Therefore, ΔABC≅ΔPQR by SSS criterion.

Since perimeter = 18cm

⇒ AB + AC + BC = 18 cm,

⇒ BC = 18 - 5 - 7 = 6 cm.

Therefore,

AB = PR = 5 cmBC = PQ = 6 cm

AC = QR = 7 cm

So, the answer is 7 cm.

### Question 4

Consider the figure below.

If ∠A=50∘, and ∠Q=60∘, then find the value of ∠B (in degrees).

#### SOLUTION

Solution :In the given figure:

In ΔABC and ΔPQR

AB = PR (Given)

BC = PQ (Given)

AC = QR (Given)

Therefore, ΔABC≅ΔPQR by SSS condition.

Therefore,

∠A=∠R=50∘;

∠B=∠P;

∠C=∠Q=60∘.

Using angle sum property in Δ ABC,

∠A+∠B+∠C=180∘

⇒ 50∘+∠B+60∘=180∘

⇒ ∠B=70∘

### Question 5

In the below quadrilateral ABCD, if AD = BC and ∠DAB = ∠CBA, then what is the relation between ∠ABD and ∠BAC ?

∠ABD = ∠BAC

∠ABD < ∠BAC

∠ABD > ∠BAC

∠DAB = ∠BAC

#### SOLUTION

Solution :A

In ΔABD and ΔBAC,

AD = BC (Given)

∠BAD = ∠CBA (Given)

AB = BA (Side common to both triangles)

Hence ΔABD≅ΔBAC

(by SAS congruence condition).

Thus, ∠ABD = ∠BAC

(congruent parts of congruent triangles).

### Question 6

If ΔDEF≅ΔBCA , then the angle of ΔBCA that corresponds to ∠E is _______ and side FD corresponds to side ________.

∠A, BC

∠B, AB

∠C, AB

Both ∠C and ∠A, BC

#### SOLUTION

Solution :C

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

Since ΔDEF≅ΔBCA, therefore ∠E=∠C and FD=AB.

### Question 7

In ΔABC and ΔPQR , AB = 4 cm, BC = 5 cm, AC = 6 cm and PQ = 4 cm, QR = 5 cm, PR = 6 cm, then which of the following is true?

ΔABC≅ΔRQP

ΔABC≅ΔQRP

ΔABC≅ΔPQR

ΔBAC≅ΔPQR

#### SOLUTION

Solution :C

In ΔABC and ΔPQR

AB = PQ = 4cm , (Given)

BC = QR = 5 cm, (Given)

AC = PR = 6 cm; (Given)

Hence, ΔABC≅ΔPQR (By SSS criterion).

### Question 8

If ΔABC≅ΔPQR, then AB is equal to ___.

PR

QR

PQ

Both PR and QR

#### SOLUTION

Solution :C

Since ΔABC≅ΔPQR,

corresponding sides of congruent triangles will be equal.

Hence, AB = PQ.

### Question 9

All the following are criteria for measuring the congruency of triangles except the _____.

SAS

SSS

ASA

AAA

#### SOLUTION

Solution :D

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.

### Question 10

Two triangles are congruent if they have

Same name

Equal measures

Same shape

Same direction

#### SOLUTION

Solution :B and C

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.