#### Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

# 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 Δ ABC and Δ DEF

AB = DE = 4.5 cm (Side)

BC = EF = 6 cm (Side) and

AC = DF = 4 cm (Side)

Therefore, by SSS criterion of congruence, ΔAB≅ ΔDEF

2)

In Δ ACB and Δ ADB

AC = AD (Side)

BC = BD (Side) and

AB = AB (Side)

Therefore, by SSS criterion of congruence, ΔAC≅ ΔADB

3) In Δ ABD and Δ FEC,

AB = FE (Side)

AD = FC (Side)

BD = CE (Side)

Therefore, by SSS criterion of congruence, ΔAB≅ ΔFEC

4) In Δ ABO and Δ DOC,

AB = DC (Side)

AO = OC (Side)

BO = OD (Side)

Therefore, by SSS criterion of congruence, ΔAB≅ ΔODC

### Question: 2

In figure, AD = DC and AB = BC

(i) Is ΔAB≅ ΔCBD?

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

### Solution:

Yes ΔABD = ΔCBD by the SSS criterion. We have used the three conditions in the SSS criterion as follows:

AB = BC and

DB = BD

### Question: 3

In Figure, AB = DC and BC = AD.

(i) Is ΔABC ΔCDA?

(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

and AC = AC

Therefore by SSS ΔABC ΔCDA

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 ΔPQR ΔEFD,

(i) Which side of ΔPQR equals ED?

(ii) Which angle of ΔPQR equals angle E?

### Solution:

ΔPQR ΔEFD

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

(ii) QPR = FED since the corresponding angles of congruent triangles are equal.

### 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:

We have AB = AC in isosceles ΔABC

And PQ = PR in isosceles ΔPQR.

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

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

Hence, ΔAB≅ ΔPQR

Now

ABC = PQR (Since triangles are congruent)However, ΔPQR is isosceles.

Therefore, PRQ = PQR = ∠ABC = 50°

### Question: 6

ABC and DBC are both isosceles triangles on a common base BC such that A and D lie on the same side of BC. Are triangles ADB and ADC congruent? Which condition do you use? If ∠BAC = 40° and BDC = 100°, then find ADB.

### Solution:

BAD = 40°/2 =20°

ABC + BCA + BAC = 180° (Angle sum property)

Since ΔABC is an isosceles triangle,

ABC = BCA ABC +ABC + 40°= 180°

2 ABC = 180° – 40° = 140° ABC = 140°/2 = 70°

DBC +  BCD + BDC = 180° (Angle sum property)

Since ΔABC is an isosceles triangle, DBC = BCD DBC + DBC + 100o = 180°

2 DBC = 180° – 100o = 80°

DBC = 80°/2 = 40°

ABD + BAD + ADB = 180°(Angle sum property)

30° + 20° + ADB = 180° (ADB = ABC – DBC), ADB = 180°- 20° – 30°

### Question: 7

Δ ABC and ΔABD are on a common base AB, and AC = BD and BC = AD as shown in Figure. Which of the following statements is true?

(i) ΔAB≅ ΔABD

### Solution:

In ΔABC and ΔBAD we have,

AC = BD (given)

BC = AD (given)

and AB = BA (common)

Therefore by SSS criterion of congruency, ΔAB≅ ΔBAD

There option (iii) is true.

### Question: 8

In Figure, ΔABC is isosceles with AB = AC, D is the mid-point of base BC.

(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, ΔABC is isosceles with AB = AC. State if ΔAB≅ ΔACB. If yes, state three relations that you use to arrive at your answer.

### Solution:

Yes, ΔAB≅ ΔACB by SSS condition.

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 ABD equal ACD? Why or why not?

### Solution:

Yes,

Given,

Δ ABC and Δ DBC have side BC common, AB = BD and AC = CD

By SSS criterion of congruency, ΔAB≅ ΔDBC

No, ABD and ACD are not equal because AB AC

### Course Features

• Video Lectures
• Revision Notes
• Previous Year Papers
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Test paper with Video Solution