ML Aggarwal Solutions for Class 7 Maths Chapter 12 Congruence of Triangles are given for easy understanding of the key concepts present in this chapter. The solutions are designed in such a manner that the students will be able to grasp the concepts easily. This chapter mainly deals with problems based on the Congruence of Triangles. For a better understanding of the concepts, students can solve the exercise problems using the ML Aggarwal Solutions. All the solutions are designed by subject experts at BYJUâ€™S, according to the latest ICSE guidelines. Using this resource on a regular basis, students can achieve high scores in their examinations.

Chapter 12 Congruence of Triangles gives answers to questions related to all the topics covered in this chapter. Further, students can refer to ML Aggarwal Class 7 Solutions PDF, which can be downloaded for free from the links given below.

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Exercise

1. If Î”ABC and Î”DEF are congruent under the correspondence ABC â†” FED, write all the corresponding congruent parts of the triangles.

Solution:

Given, Î”ABC and Î”DEF are congruent under the correspondence,

ABC â†” FED

Hence,

âˆ A â†” âˆ F, âˆ B â†” âˆ E, âˆ C â†” âˆ D

AB â†” FE, BC â†” ED and AC â†” FD

**Â **

**2. If Î”DEF = Î”BCA, then write the part(s) of Î”BCA that correspond to(i) âˆ E(ii)Â EF(iii) âˆ F(iv)Â DFSolution:**

If Î”DEF = Î”BCA, then

(i) âˆ E â†” âˆ C

(ii) EF â†” CAÂ

(iii) âˆ F â†” âˆ A

(iv) DF â†” BA

3. In the figure given below, the lengths of the sides of the triangles are indicated. By using SSS congruency rule, state which pairs of triangles are congruent. In the case of congruent triangles, write the result in symbolic form:

Solution:

(i) In the given figure,

In Î”ABC and Î”PQR, itâ€™s seen that

AB â†” PQ, BC â†” PR, and AC â†” QR

So, Î”s are congruent

Hence, Î”ABC â‰… Î”QPR

(ii) In the given figure,

In Î”ABC and Î”PQR

AC â†” PR, BC â†” PQ

But, AB â‰ QR

Hence, Î”s are not congruent.

4. In the given figure, AB = 5 cm, AC = 5 cm, BD = 2.5 cm and CD = 2.5 cm

(i) State the three pairs of equal parts in Î”ADB and Î”ADC

(ii) Is Î”ADB = Î”ADC? Give reasons.

(iii) Is âˆ B = âˆ C? Why?

Solution:

In the given figure, we have

AB = 5 cm, AC = 5 cm, BD = 2.5 cm and CD = 2.5 cm

In Î”ABD and Î”ACD,

(i) AB = AC = 5 cm

BD = CD = 2.5 cm

AD = AD (Common Side)

(ii) Hence, Î”ABD â‰… Î”ACD (By SSS axiom)

(iii)As Î”ABD â‰… Î”ACD, by C.P.C.T

we have, âˆ B = âˆ C

**Â 5. In the given figure, AB = AC and D is the mid-point ofÂ BC.(i) State the three pairs of equal parts in Î”ADB and Î”ADC.(ii) Is Î”ADB = Î”ADC? Give reasons.(iii) Is âˆ B = âˆ C? Why?Solution:**

(i) In Î”ABC, we have

AB = AC

And, D is the mid-point of BC

BD = DC

Now, in Î”ADB and Î”ADC

AB = AC (Given)

AD = AD (Common)

BD = DC (D is mid-point of BC)

(ii) Î”ADB â‰… Î”ADC by SSS axiom

(iii) By c.p.c.t.,

âˆ B = âˆ C

6. In the figure given below, the measures of some parts of the triangles are indicated. By using SAS rule of congruency, state which pairs of triangles are congruent. In the case of congruent triangles, write the result in symbolic form.

Solution:

(i) In Î”ABC and Î”DEF, we have

AB = DE (Each = 2.5 cm)

AC = DF (Each = 2.8 cm)

But, âˆ A â‰ âˆ D (Have different measure)

Hence, Î”ABC is not congruent to Î”DEF.

(ii) In Î”ABC and Î”RPQ, we have

AC = RP (Each = 2.5 cm)

CB = PQ (Each = 3 cm)

âˆ C = âˆ P (Each = 35Â°)

Hence,

Î”ACB and Î”RPQ are congruent by SAS axiom of congruency.

(iii) In Î”DEF and Î”PQR, we have

FD = QP (Each = 3.5 cm)

FE = QR (Each = 3 cm)

âˆ F = âˆ Q (Each 40Â°)

Hence, Î”DEF and Î”PQR are congruent by SAS axiom of congruency.

(iv) In Î”ABC and Î”PRQ, we have

AB = PQ (Each = 4 cm)

BC = QR (Each = 3 cm)

But, included angles B and âˆ Q are not equal

Hence, Î”ABC and Î”PQR are not congruent to each other.

7. By applying SAS congruence rule, you want to establish that Î”PQR = Î”FED. If is given that PQ = EF and RP = DF. What additional information is needed to establish the congruence?

Solution:

In Î”PQR and Î”FED, we have

PQ = FE

RP = DF

Now, their included angles âˆ P must be equal to âˆ F for congruency.

Thus, âˆ P = âˆ F.