## RD Sharma Solutions for Class 6 Chapter 15 Pair of Lines and Transversal Free Online

Exercise 15.1 page: 15.2

**1. Identify parallel line segments shown in Fig. 15.6.**

**Solution:**

(i)

**From the figure we know that BC || DE.**
(ii) From the figure we know that AB || DC, AD || BC.

(iii) From the figure we know that AB || DC and AD || BC.

(iv) From the figure we know that PQ || TS, UT || QR and UP || SR.

(v) From the figure we know that AB || EF || CD, BC || AD and CF || DE.

(vi) From the figure we know that EF || BC, AB || DF and AC || DE.

**2. Name the pairs of all possible parallel edges of the pencil box whose figure is shown in Fig. 15.7.**

**Solution:**

The pairs of all possible parallel edges of the pencil box are

AB || DC || HE || GF and AD || GH || BC || EF

**3. In Fig. 15.8, do the segments AB and CD intersect? Are they parallel? Give reasons.**

**Solution:**

No, AB and CD do not intersect but they can intersect if extended further. No AB and CD are not parallel since, the distance between them is not constant.

**4. State which of the following statements are true (T) or which are false (F):**

**(i) If two lines in the same plane do not intersect, then they must be parallel.**

**(ii) Distance between two parallel lines is not same everywhere.**

**(iii) If m ⊥ l, n ⊥ l and m ≠ n, then m || n.**

**(iv) Two non-intersecting coplanar rays are parallel.**

**(v) If ray AB || line m, then line segment AB.**

**(vi) If line AB || line m, then line segment AB || m.**

**(vii) No two parallel line segments intersect.**

**(viii) Every pair of lines is a pair of coplanar lines.**

**(ix) Two lines perpendicular to the same line are parallel.**

**(x) A line perpendicular to one of two parallel lines is perpendicular to the other.**

**Solution:**

(i) True

(ii) False

(iii) True

(iv) False

(v) True

(vi) True

(vii) True

(viii) False

(ix) True

(x) True

Exercise 15.2 page: 15.6

**1. In Fig. 15.17, line n is a transversal to lines l and m. Identify the following:**

**(i) Alternate and corresponding angles in Fig. 15.17 (i).**

**(ii) Angles alternate to ∠d and ∠g and angles corresponding to ∠f and ∠h in Fig. 15.17 (ii).**

**(iii) Angle alternative to ∠PQR, angle corresponding to ∠RQF and angle alternate to ∠PQE in Fig. 15.17 (iii).**

**(iv) Pairs of interior and exterior angles on the same side of the transversal in Fig. 15.17 (ii).**

**Solution:**

(i)

**Alternate interior angles are ∠BGH and ∠CHG; ∠AGH and ∠CHF**
Alternate exterior angles are ∠AGE and ∠DHF; ∠EGB and ∠CHF

Corresponding angles are ∠EGB and ∠GHD; ∠EGA and ∠GHC; ∠BGH and ∠DHF; ∠AGF and ∠CHF.

(ii) Angles alternate to ∠d and ∠g are ∠e and ∠b and angles corresponding to ∠f and ∠h are ∠c and ∠a.

(iii) From the figure we know that l is transversal to m and n.

Angle alternate to ∠PQR is ∠QRA

Angle corresponding to ∠RQF is ∠BRA

Angle alternate to ∠PQE is ∠BRA

(iv) Interior angles are ∠d, ∠f and ∠a, ∠e and exterior angles are ∠c, ∠g and ∠b, ∠h

**2. Match column A and column B with the help of the Fig. 15.18:**

**Column A Column B**

**(i) Vertically opposite angles (i) ∠PAB and ∠ABS**

**(ii) Alternate angles (ii) ∠PAB and ∠RBY**

**(iii) Corresponding angles (iii) ∠PAB and ∠XAQ**

**Solution:**

(i) ∠PAB and ∠XAQ are vertically opposite angles

(ii) ∠PAB and ∠ABS are alternate angles

(iii) ∠PAB and ∠RBY are corresponding angles