RS Aggarwal Solutions for Class 7 Maths Chapter 16 – Congruence are given here in a simple but comprehensive way. Congruence solutions are extremely helpful for the students to clear all their doubts easily and understand the basics of this chapter more effectively. Students of Class 7 are suggested to solve RS Aggarwal Class 7 Solutions to strengthen the fundamentals and be able to solve questions that are usually asked in the examination.

These Ratio and Proportion solutions are available for download in pdf format and provide solutions to all the questions provided in Class 7 Maths Chapter 16 wherein problems are solved step by step with detailed explanations. Download pdf of Class 7 Chapter 16 in their respective links.

## Download PDF of RS Aggarwal Solutions for Class 7 Maths Chapter 16 – Congruence

### Access answer to chapter 16 – Congruence

Exercise 16 Page: 199

**1. State the correspondence between the vertices, sides and angles of the following pairs of congruent triangles.**

**(i). Î”ABC â‰… Î”EFD **

**Solution:-**

Two triangles are congruent if pairs of corresponding sides and corresponding angles are equal.

If we write Î”ABC â‰… Î”EFD, it would mean that,

Correspondence between vertices:

A â†” E, B â†” F, C â†” D

Correspondence between sides:

AB = EF, BC = FD, CA = DE

Correspondence between angles:

âˆ A = âˆ E, âˆ B = âˆ F, âˆ C = âˆ D

**(ii). Î”CAB â‰… Î”QRP **

**Solution:-**

Two triangles are congruent if pairs of corresponding sides and corresponding angles are equal.

If we write Î”CAB â‰… Î”QRP, it would mean that,

Correspondence between vertices:

C â†” Q, A â†” R, B â†” P

Correspondence between sides:

CA = QR, AB = RP, BC = PQ

Correspondence between angles:

âˆ C = âˆ Q, âˆ A = âˆ R, âˆ B = âˆ P

**(iii). Î”XZY â‰… Î”QPR **

**Solution:-**

Two triangles are congruent if pairs of corresponding sides and corresponding angles are equal.

If we write Î”XZY â‰… Î”QPR, it would mean that,

Correspondence between vertices:

X â†” Q, Z â†”P, Y â†” R

Correspondence between sides:

XZ = QP, ZY = PR, XY = QR

Correspondence between angles:

âˆ X = âˆ Q, âˆ Z = âˆ P, âˆ Y = âˆ R

**(iv). Î”MPN â‰… Î”SQR **

**Solution:-**

Two triangles are congruent if pairs of corresponding sides and corresponding angles are equal.

If we write Î”MPN â‰… Î”SQR, it would mean that,

Correspondence between vertices:

M â†” S, P â†” Q, N â†” R

Correspondence between sides:

MP = SQ, PN = QR, MN = SR

Correspondence between angles:

âˆ M = âˆ S, âˆ P = âˆ Q, âˆ N = âˆ R

**2. Given below are pairs of congruent triangles. State the property of congruence and name the congruent triangles in each case.**

**(i). **

**Solution:-**

SAS congruence property:- Two triangles are congruent if the two sides and the included angle of one are respectively equal to the two sides and the included angle of the other.

Î”ACB â‰… Î”DEF

**(ii). **

**Solution:-**

RHS congruence property:- Two right triangles are congruent if the hypotenuse and one side of the first triangle are respectively equal to the hypotenuse and one side of the second.

Î”RPQ â‰… Î”LNM

**(iii).**

**Solution:-**

SSS congruence property:- Tow triangles are congruent if the three sides of one triangle are respectively equal to the three sides of the other triangle.

Î”YXZ â‰… Î”TRS

**(iv).**

**Solution:-**

ASA congruence property:- Two triangles are congruent if the two angles and the included side of one are respectively equal to the two angles and the included side of the other.

Î”DEF â‰… Î”PNM

**(v).**

**Solution:-**

ASA congruence property:- Two triangles are congruent if the two angles and the included side of one are respectively equal to the two angles and the included side of the other.

Î”ACB â‰… Î”ACD

**3. In Fig. (i), PL âŠ¥ OA and PM âŠ¥ OB such that PL = PM. Is Î”PLO â‰… Î”PMO?**

**Give reasons in support of your answer.**

**Solution:-**

From the question:-

Is given that PL âŠ¥ OA, PM âŠ¥ OB and PL = PM

To prove:

Î”PLO â‰… Î”PMO

Proof:

From the fig,

In Î”PLO and Î”PMO,

âˆ PLO = âˆ PMO = 90^{O}

PO = PO (common side)

PL = PM (given)

âˆ´ Î”PLO â‰… Î”PMO

Yes. Î”PLO â‰… Î”PMO by the RHS congruence property

**4. In fig. (ii), AD = BC and AD âˆ¥ BC. Is AB = DC? Give reasons in support of your answer.**

**Solution:-**

From the question,

Is given that AD = BC and AD âˆ¥ BC

To prove:

AB = DC

Proof:

In Î”ABC and Î”CDA,

BC = DA (given)

AD âˆ¥ BC (given)

âˆ BCA = âˆ DAC (alternate angles)

AC = AC (common)

âˆ´ Î”ABC â‰… Î”CDA

AB = CD

Yes. AB = CD by the SAS congruence property.

**5. In the adjoining figure, AB = AC and BD = DC. Prove that Î”ADB â‰… Î”ADC and hence show that **

**(i) âˆ ADB = âˆ ADC = 90 ^{o}, (ii) âˆ BAD = âˆ CAD. **

**Solution:-**

Given,

AB = AC and BD = DC

To prove,

Î”ADB â‰… Î”ADC

Proof,

In the right triangles ADB and ADC, we have:

Hypotenuse AB = Hypotenuse AC (given)

BD = DC (given)

AD = AD (common)

âˆ´ Î”ADB â‰… Î”ADC

By SSS congruence property:

âˆ ADB = âˆ ADC (corresponding parts of the congruent triangles) â€¦ (1)

âˆ ADB and âˆ ADC are on the straight line.

âˆ´âˆ ADB + âˆ ADC =180^{o}

âˆ ADB + âˆ ADB = 180^{o}

2 âˆ ADB = 180^{o}

âˆ ADB = 180/2

âˆ ADB = 90^{o}

From (1):

âˆ ADB = âˆ ADC = 90^{o}

(ii) âˆ BAD = âˆ CAD (âˆµ corresponding parts of the congruent triangles)

**6. In the adjoining figure, ABC is a triangle in which AD is the bisector of âˆ A. If AD âŠ¥BC, show that Î”ABC is isosceles.**

**Solution:-**

Given:

AD is the bisector of âˆ A

So we have, âˆ DAB = âˆ DAC â€¦ (1)

AD âŠ¥BC

So we have, âˆ BDA = âˆ CDA = 90^{o}

To prove,

Î”ABC is isosceles.

Proof,

In Î”DAB and Î”DAC,

âˆ BDA = âˆ CDA = 90^{o}

DA = DA (common)

âˆ DAB = âˆ DAC (from 1)

By ASA congruence property,

Î”DAB â‰… Î”DAC

AB = AC

Hence, Î”ABC is isosceles.

**7. In the adjoining figure, AB = AD and CB = CD. Prove that Î”ABC â‰… Î”ADC.**

**Solution:-**

Given,

AB = AD and CB = CD

To prove,

Î”ABC â‰… Î”ADC.

Proof,

In Î”ABC and Î”ADC

AB = AD (given)

CB = CD (given)

AC = AC (common)

âˆ´ Î”ABC â‰… Î”ADC.

(By SSS congruence property)

**8. In the given figure, PA âŠ¥ AB, QB âŠ¥ AB and PA = QB. Prove that Î”OAP = Î”OBQ. Is OA =OB?**

**Solution:-**

Given,

PA âŠ¥ AB, QB âŠ¥ AB and PA = QB

To prove,

Î”OAP = Î”OBQ

Is OA =OB?

Proof,

In Î”OAP and Î”OBQ

PA = QB (given)

âˆ POA = âˆ QOB (vertically opposite angles)

âˆ OAP = âˆ OBQ = 90^{o}

From AAS congruence property,

Î”OAP â‰… Î”OBQ

Then,

OA = OB (corresponding parts of the congruent triangles)

**9. In the given figure, triangles ABC and DCB are right-angled at A and D respectively and AC = DB. Prove that Î”ABC = Î”DCB.**

**Solution:-**

Given,

Triangles ABC and DCB are right-angled at A and D respectively.

AC = DB

To prove,

Î”ABC = Î”DCB

Proof,

In Î”ABC and Î”DCB:

AC = DB (given)

BC = BC (common)

âˆ CAB = âˆ BDC = 90^{o}

From the RHS congruence property,

Î”ABC â‰… Î”DCB.

## RS Aggarwal Solutions for Class 7 Maths Chapter 16 – Congruence

Chapter 16 – Congruence contains 1 exercise and the RS Aggarwal Solutions available on this page provide solutions to the questions present in the exercises. Now, let us have a look at some of the essential concepts discussed in this chapter.

- Congruent Figures
- Types of Congruent Figures
- Congruence of Triangles
- Congruence and Area

### Chapter Brief of RS Aggarwal Solutions for Class 7 Maths Chapter 16 – Congruence

RS Aggarwal Solutions for Class 7 Maths Chapter 16 – Congruence. Every figure has a shape, size and a position. If we are given two figures then by simply looking at them carefully we can decide whether they are of the same shape or not. The solutions are solved in such a way that students will understand clearly.