**Congruence Exercise 16.2**

**Question: 1**

In the following pairs of triangle (Figures), the lengths of the sides are indicated along sides. By applying SSS condition, determine which are congruent. State the result in symbolic.

**Solution:**

1) In

AB = DE = 4.5 cm (Side)

BC = EF = 6 cm (Side) and

AC = DF = 4 cm (Side)

Therefore, by SSS criterion of congruence,

2)

In

AC = AD (Side)

BC = BD (Side) and

AB = AB (Side)

Therefore, by SSS criterion of congruence,

3) In

AB = FE (Side)

AD = FC (Side)

BD = CE (Side)

Therefore, by SSS criterion of congruence,

4) In

AB = DC (Side)

AO = OC (Side)

BO = OD (Side)

Therefore, by SSS criterion of congruence,

**Question: 2**

In figure, AD = DC and AB = BC

(i) Is

(ii) State the three parts of matching pairs you have used to answer (i).

**Solution:**

Yes

AD = DC

AB = BC and

DB = BD

**Question: 3**

In Figure, AB = DC and BC = AD.

(i) Is

(ii) What congruence condition have you used?

(iii) You have used some fact, not given in the question, what is that?

**Solution:**

We have AB = DC

BC = AD

and AC = AC

Therefore by SSS

We have used Side congruence condition with one side common in both the triangles.

Yes, have used the fact that AC = CA.

**Question: 4**

In

(i) Which side of

(ii) Which angle of

**Solution:**

(i) Therefore PR = ED since the corresponding sides of congruent triangles are equal.

(ii)

**Question: 5**

Triangles ABC and PQR are both isosceles with AB = AC and PO = PR respectively. If also, AB = PQ and BC = QR, are the two triangles congruent? Which condition do you use?

It ∠B = 50°, what is the measure of ∠R?

**Solution:**

And PQ = PR in isosceles

Also, we are given that AB = PQ and QR = BC.

Therefore, AC = PR (AB = AC, PQ = PR and AB = PQ)

Hence,

Now

Therefore,

**Question: 6**

**Solution:**

^{o }= 180°

^{o} = 80°

**Question: 7**

(i)

(ii)

(iii)

**Solution:**

In

AC = BD (given)

BC = AD (given)

and AB = BA (common)

Therefore by SSS criterion of congruency, ΔABC ≅ ΔBAD

There option (iii) is true.

**Question: 8**

In Figure,

(i) Is

(ii) State the three pairs of matching parts you use to arrive at your answer.

**Solution:**

We have AB = AC.

Also since D is the midpoint of BC, BD = DC

Also, AD = DA

Therefore by SSS condition,

We have used AB, AC : BD, DC AND AD, DA

**Question: 9**

In figure,

**Solution:**

Yes,

Since, ABC is an isosceles triangle, AB = BC, BC = CB and AC = AB

**Question: 10**

Triangles ABC and DBC have side BC common, AB = BD and AC = CD. Are the two triangles congruent? State in symbolic form, which congruence do you use? Does

**Solution:**

Yes,

Given,

By SSS criterion of congruency,

No,