The DAV Class 7 Maths Book Solutions and **DAV Class 7 Maths Chapter 13 Worksheet 2** Solutions of Symmetry offer comprehensive answers to textbook questions.

## DAV Class 7 Maths Ch 13 WS 2 Solutions

Question 1.

Find the line of symmetry of any 3 line segments on different sheets of paper.

Answers:

Draw the perpendicular bisectors of the line segment which is the line of symmetry of the line segment. In above figures;

l_{1} is the line of symmetry of \(\overline{\mathrm{AB}}\)

l_{2} is the line of symmetry of \(\overline{\mathrm{PQ}}\)

and l_{3} is the line of symmetry of \(\overline{\mathrm{MN}}\).

Question 2.

Check if the dotted lines are the line of symmetry of the given line segments.

Answer:

(i) The dotted line is not the perpendicular bisector of PQ, so it is not a line of symmetry.

(ii) The dotted line is the perpendicular bisector of XY, so it is a line of symmetry.

Question 3.

Lines l and m are the lines of symmetry of the line segments XY and YZ respectively. If XA = 4 cm and YZ = 6 cm, find AY, YB, XZ.

Answer:

l is the line of symmetry of XY.

∴ XA = AY

⇒ 4 = AY

⇒ AY = 4 cm

m is the line of symmetry of YZ, YZ = 6 cm

∴ YB = BZ = \(\frac{6}{2}\) = 3 cm

XZ = 2XA + YZ = 2(4) + 6 = 8 + 6 = 14 cm

Hence, AY = 4 cm, YB = 3 cm and XZ = 14 cm

Question 4.

Find the line of symmetry of the following angles on different sheets of paper.

(a) 60°

(b) 150°

(c) 45°

Answer:

(a) OP is the bisector of ∠AOB, so it is the line of symmetry of ∠AOB where ∠AOB = 60°

(b) SQ is the bisector of ∠RST, so it is the line of symmetry of ∠RST, where ∠RST = 150°

(c) NL is the bisector of ∠MNO, so it is the line of symmetry of ∠MNO, where ∠MNO = 45°.

Question 5.

If dotted lines represent the lines of symmetry of the given angles, find x in each case.

Answer:

In fig. (z) The dotted line is the bisector of the angle

x = \(\frac{80^{\circ}}{2}\) = 40°

In figure (ii) the dotted line is the bisector of the angle

x = 2 × 55° = 110°

Question 6.

The dotted line represents the line of symmetry of ΔABC. If ∠ABC = 40° and OB = 4.5 cm, find.

(a) ∠BAO

(b) Measure of OC. Give reasons.

Answer:

(a) In ΔABC, OA is the line of symmetry 8

∴ ΔABC is an isosceles triangle ∠B = ∠C

∠A + ∠B + ∠C = 180°

∠A + 40° + 40° = 180°

∴ ∠A = 180° – 80° = 100°

AO is the line of symmetry

AO is the bisector of ∠A

∴ ∠BAO = \(\frac{100^{\circ}}{2}\) = 50°

(b) OA is the line of symmetry of BC

OA is the perpendicular bisector of BC BO = OC = 4.5 cm

Hence, ∠BAO = 50° and OC = 4.5 cm

Question 7.

Construct an equilateral ΔABC of side 4 cm. Find all its line of symmetry.

Answer:

Draw ΔABC in which AB = BC = AC = 4 cm.

Draw the bisectors of ∠A, ∠B and ∠C

Al, Bm and Cn are the line of symmetry of an equilateral ΔABC.

Question 8.

Will a scalene triangle have any line of symmetry?

Answer:

No, scalene triangle has no line of symmetry.

Question 9.

Under what circumstances will a right angled triangle have a line of symmetry? Give reasons.

Answer:

A right angled triangle will have a line of symmetry if it is an isosceles right triangle. Because the triangle cannot be an equilateral triangle and scalene triangle has no line of symmetry.

Question 10.

Can a right angled triangle have more than one line of symmetry under any circumstances?

Answer:

No, right angled triangle will have only one line of symmetry only if it is isosceles triangle.