Punjab State Board PSEB 7th Class Maths Book Solutions Chapter 7 Congruence of Triangles Ex 7.1 Textbook Exercise Questions and Answers.

## PSEB Solutions for Class 7 Maths Chapter 7 Congruence of Triangles Ex 7.1

1. Identify the pairs of congruent figures and write the congruence in symbolic form.

Question (i).

Answer:

In figure

Radius of circle C_{1} = 2 cm

Radius of circle C_{2} = 1.5 cm

As radius of circle C_{1} ≠ Radius of circle C_{2}

∴ Circle C_{1} is not congruent to circle C_{2}

Question (ii).

Answer:

In figure

Length of line segment AB = 6 cm

Length of line segment MN = 7 cm

As length of line segment AB ≠ Length of line segment MN

∴ AB is not congruent to MN

Question (iii).

Answer:

In ΔXYZ and ΔPQR

XY = PQ, YZ = PR, XZ = QR

So, ΔXYZ and ΔPQR have the same size and shape

∴ ΔXYZ ≅ ΔQPR

Question (iv).

Answer:

In figure ΔABC and ΔDEF do not have the same size and shape

∴ ΔABC and ΔDEF are do not have the same size and shape.

∴ ΔABC and ΔDEF are not-congruent.

Question (v).

Answer:

Question (vi).

Answer:

2. If ΔPQR as ΔOMN under the correspondence PQR ↔ OMN, write all the corresponding congruent parts of the triangle.

Solution:

For better understanding of the correspondence, let us draw a diagram of given correspondence.

The correspondence is PQR → OMN

This means vertices P ↔ O, Q ↔ M, R ↔ N

Sides : PQ ↔ OM, QR ↔ MN, RP ↔ NO

and Angles: ∠PQR ↔ ∠OMN, ∠QRP ↔ ∠MNO, ∠RPQ ↔ ∠NOM

3. Draw any two pairs of congruent triangles.

Solution:

Two pairs of congruent triangles are :

(i) Draw a ΔABC in which AB = 5 cm, BC = 4 cm and CA = 6 cm.

Draw another ΔPQR in which PQ = 6 cm, QR = 5 cm and RP = 4 cm shown in the following figure.

Make a trace copy of ΔABC using a tracig paper and superinpose it on ΔPQR, where C falls on P, A falls on Q and B falls on R. We observe that ΔABC will corr. ΔPQR.

∴ ΔABC ≅ ΔQRP

(ii) Draw a ΔXYZ in which XY = 5 cm, YZ = 6 cm and ZX = 3 cm. Draw another ΔLMN in which LM = 5 cm, MN = 6 cm and NL = 3 cm. Since both ΔXYZ and ΔLMN have the same size and shape.

4. If ΔABC ≅ ΔZYX, write the parts of ΔZYX that correspond to.

(i) ∠B

(ii) CA

(iii) AB

(iv) ∠C

Solution:

First of all we draw a diagram of given correspondence.

The correspondence is ABC ↔ ZYX.

This means A ↔ Z, B ↔ Y, C ↔ X

Therefore

(i) ∠B = ∠Y

(ii) CA = XZ

(iii) AB = ZY

(iv) ∠C = ∠X

5. Multiple Choice Questions :

Question (i).

If ΔABC as ΔXYZ under the correspondence ABC ↔ XYZ. Then

(a) ∠A = ∠Z

(b) ∠X = ∠B

(c) ∠A = ∠X

(d) ∠C = ∠X.

Answer:

(c) ∠A = ∠X

Question (ii).

Two line segments are congruent if,

(a) They are parallel

(b) They intersect each other

(c) They are part of same line

(d) They are of equal length.

Answer:

(d) They are of equal length.

Question (iii).

Two triangles ΔABC and ΔLMN are congruent AB = LM, BC = MN. If AC = 5 cm then LN is :

(a) 3 cm

(b) 15 cm

(c) 5 cm

(d) Can’t find.

Answer:

(c) 5 cm

6. Two right angles are always congruent. (True/False)

Answer:

True

7. Two opposite sides of a rectangle are always congruent. (True/False)

Answer:

True