RS Aggarwal Solutions for Class 6 Chapter 17 Quadrilaterals

 

Exercise 17.1

 

Question 1. List any four symmetrical objects from your home or school. Also mention the line of symmetry.
Answer: Four symmetrical objects with their lines of symmetry are:
(i) A gate - has one vertical line of symmetry
(ii) A green board - has one vertical line of symmetry
(iii) A pair of spectacles - has one vertical line of symmetry
(iv) A glass - has one vertical line of symmetry
In simple words: Find everyday items at home or school that look the same on both sides when you fold them in half. Mark the fold line - that's the line of symmetry.

Exam Tip: Always identify objects with clear left-right or top-bottom balance; draw the line of symmetry vertically or horizontally through the middle.

 

Question 2. Identify the symmetrical instruments from your mathematical instrument box.
Answer: The symmetrical instruments from a mathematical instrument box are:
(i) A protractor - has one vertical line of symmetry
(ii) A divider - has one vertical line of symmetry
(iii) A ruler (scale) - has one vertical line of symmetry
(iv) A glass - has one vertical line of symmetry
(v) A pencil - has one vertical line of symmetry
In simple words: Look at each tool in your geometry box and check if one half mirrors the other half perfectly when folded down the middle.

Exam Tip: Focus on instruments with clear bilateral symmetry; sketching the symmetry line helps verify your answer.

 

Question 3. Copy each of the following on a squared paper and compute then in such a way that the dotted line is the line of symmetry.
Answer: To complete each shape so the dotted line becomes the line of symmetry:
(i) Draw a matching triangle pointing left to mirror the right-pointing triangle
(ii) Draw the upper half of the shape to match the lower half below the dotted line
(iii) Draw the left portion of the staircase shape to mirror the right portion
(iv) Draw the upper triangle and rectangle to match the lower parts across the vertical dotted line
(v) Draw the right half of the pentagon to match the left half on the other side of the dotted line
(vi) Draw the matching portions of the hexagon shape across the diagonal dotted line
In simple words: For each incomplete figure, draw the missing parts on the other side of the dotted line so both sides look exactly the same - like a mirror image.

Exam Tip: Count grid squares carefully when transferring the shape to the opposite side; ensure all edges and corners align perfectly across the symmetry line.

 

Exercise 17.2

 

Question 1. Find the number of line of symmetry in each of the following shapes
(i) A four-pointed star
(ii) An insect body shape
(iii) Two squares arranged diagonally
(iv) A flower shape with rounded petals
(v) A pine tree shape
Answer:
(i) A four-pointed star has 4 lines of symmetry
(ii) An insect body shape has 1 line of symmetry
(iii) Two squares arranged diagonally have 2 lines of symmetry
(iv) A flower shape with rounded petals has 2 lines of symmetry
(v) A pine tree shape has 1 line of symmetry
In simple words: Count how many different ways you can fold each shape so the two halves match perfectly. Each fold line is one line of symmetry.

Exam Tip: Try folding the shape mentally or on paper in different directions - vertical, horizontal, and diagonal - to find all possible lines of symmetry.

 

Question 2. Copy the following drawings on a paper and compute each one of them in such a way that resulting figure has two dotted lines as two lines of symmetry:
Answer: To complete each shape with two dotted lines as lines of symmetry:
(i) Complete the right and bottom portions of the triangle shape to make it symmetric along both the vertical and horizontal dotted lines
(ii) Complete the left, top, and bottom sections of the four-pointed star shape so it mirrors across both axes
(iii) Complete the left portions of the staircase-like shape to reflect the right side across the vertical line
(iv) Complete the upper and right portions of the hexagon to achieve symmetry along both the vertical and horizontal dotted lines
(v) Complete the left and top sections of the multi-pointed star to ensure reflection across both perpendicular dotted lines
(vi) Complete the curved shape to be symmetric along both the vertical and horizontal dotted axes
In simple words: Fill in the missing parts so that each shape looks the same whether you fold it up-down or left-right along the dotted lines. Both folds should create matching halves.

Exam Tip: Work systematically - first complete one axis of symmetry, then verify that the shape also has symmetry along the perpendicular axis; use a ruler to ensure straight edges.

 

Exercise 17.3

 

Question 1. Complete the following table:

Answer: The completed table is provided above with all shapes and their corresponding number of lines of symmetry. A scalene triangle has no symmetry, an isosceles triangle has one line, an equilateral triangle has three lines, rectangles have two, parallelograms have none, rhombuses have two, lines have infinitely many, line segments have one, angles have one, isosceles trapeziums have one, kites have one, arrow heads have one, semi-circles have one, circles have infinitely many, regular pentagons have five, and regular hexagons have six lines of symmetry.
In simple words: The number of lines of symmetry depends on the shape's sides and angles. Regular shapes (all sides equal) have more lines of symmetry than irregular ones.

Exam Tip: Remember: equilateral triangles have 3 lines, squares have 4, regular pentagons have 5, regular hexagons have 6; circles and lines have infinitely many; most irregular shapes have 0 or 1.

 

Question 2. Consider the English alphabets A to Z. List among them the letters which have
(i) Vertical line of symmetry
(ii) Horizontal line of symmetry
(iii) Vertical and horizontal line of symmetry
(iv) No line of symmetry
Answer:
(i) Vertical line of symmetry: A, H, I, M, O, T, U, V, W, X, Y
(ii) Horizontal line of symmetry: B, C, D, E, H, I, K, O, X
(iii) Vertical and horizontal line of symmetry: H, I, O, X
(iv) No line of symmetry: F, G, J, L, N, P, Q, R, S, Z
In simple words: Some letters look the same when folded left to right (vertical symmetry), some when folded top to bottom (horizontal symmetry), and a few have both. Others don't fold into matching halves at all.

Exam Tip: Visualize folding each letter on paper or mentally check the shape carefully; H, I, O, and X are the only capitals with both vertical and horizontal symmetry.

 

Question 3. No line of symmetry?
(i) Exactly one line of symmetry.
(ii) Exactly two line of symmetry.
(iii) Three line of symmetry.
(iv) no lines of symmetry
Answer: (i) Exactly one line of symmetry: Yes; Isosceles triangle

Exam Tip: Always count the lines of symmetry carefully by checking if the shape folds perfectly onto itself along that line. An isosceles triangle has exactly one such line.

 

Question 4. On a squared paper, sketch the following:
(i) A triangle with a horizontal with both horizontal and vertical line of symmetry
(ii) A quadrilateral with both horizontal and vertical lines of symmetry
(iii) A quadrilateral with horizontal but no vertical lines of symmetry
(iv) A hexagon with exactly two lines of symmetry
(v) A hexagon with exactly six lines of symmetry
Answer: The sketches are provided in the solution table below, showing each figure with its corresponding symmetry lines marked with dashed lines:

Exam Tip: When sketching symmetry lines, use dashed lines and ensure they divide the shape into two identical halves. Remember that horizontal means left-right and vertical means top-bottom.

 

Question 5. Draw neat diagrams showing the line (or lines) of symmetry and give the specific name to the quadrilateral having:
(i) only one line of symmetry. How many such quadrilaterals are there?
(ii) Its diagonals as the only lines of symmetry
(iii) two lines of symmetry other than diagonals
(iv) More than two lines of symmetry
Answer:
(i) only one line of symmetry: There are three quadrilaterals with exactly one line of symmetry: Kite, Arrow head, and Isosceles trapezoid.

(ii) diagonals as the only lines of symmetry: The Rhombus has its diagonals as the only lines of symmetry.

(iii) two lines of symmetry other than diagonals: The Rectangle has two lines of symmetry - one vertical and one horizontal line - that are not its diagonals.

(iv) More than two lines of symmetry: The Square and regular polygons with more than four sides have more than two lines of symmetry.

Exam Tip: Distinguish carefully between symmetry lines that pass through diagonals and those that are perpendicular bisectors of sides. A kite and rhombus look similar but differ in their symmetry properties.

 

Question 6. write the specific names of all the three quadrilaterals which have only one line of symmetry
Answer: The three quadrilaterals having exactly one line of symmetry are:

(1) Kite - has one vertical line of symmetry
(2) Arrow head - has one vertical line of symmetry
(3) Isosceles trapezoid - has one vertical line of symmetry

Exam Tip: These three shapes all have one symmetry line that runs vertically through the middle. Make sure you can sketch each one and mark its line of symmetry clearly.

 

Question 7. Trace each of the following figures and draw the lines of symmetry. If any
(i) Triangle
(ii) Two diamonds stacked
(iii) Pentagon
(iv) Square with grid lines
(v) Octagon
(vi) Four-pointed star
Answer: The solution shows each figure with its lines of symmetry drawn as dashed lines:

(i) Triangle - one vertical line of symmetry through the top vertex
(ii) Two diamonds - two vertical and two diagonal lines of symmetry
(iii) Pentagon - one horizontal line of symmetry
(iv) Square with grid - four lines of symmetry (two vertical/horizontal, two diagonal)
(v) Octagon - multiple lines of symmetry (vertical, horizontal, and diagonal)
(vi) Four-pointed star - four lines of symmetry extending from the center

Exam Tip: When drawing symmetry lines, fold your tracing paper mentally along each line to check if the two halves match perfectly. This confirms whether the line is actually a line of symmetry.

 

Question 8. On squared paper copy the triangle in each of the following figures. In each case draw the line(s) of symmetry if any and identify the type of the triangle
(i) Triangle with one vertical line
(ii) Triangle with three lines crossing through center
(iii) Right-angled triangle
(iv) Triangle with one diagonal line
Answer:
(i) This shape represents an isosceles triangle because it has exactly one line of symmetry running vertically down the middle.

(ii) This is an equilateral triangle because it has three lines of symmetry, each running from a vertex through the center.

(iii) This represents a right-angled triangle because it has no line of symmetry (the right angle breaks any potential symmetry).

(iv) This is an isosceles triangle because it has one line of symmetry, even though it is tilted at an angle.

Exam Tip: Always verify triangle types by checking both the sides and the symmetry lines. An equilateral triangle always has three symmetry lines, while an isosceles has exactly one.

 

Question 9. Find the lines of symmetry for each of the following shapes
(i) Concentric squares
(ii) Oval (divided horizontally)
(iii) Swastika symbol
(iv) Flower with six petals
(v) Robot/figure with triangles
(vi) Regular hexagon
(vii) Pentagon outline
(viii) Scissors shape
Answer: The solution table displays each shape with its lines of symmetry marked as dashed lines:

(i) Concentric squares - four lines of symmetry (two through opposite corners, two through midpoints of opposite sides)
(ii) Oval - two lines of symmetry (one vertical through the center, one horizontal through the center)
(iii) Swastika - four lines of symmetry (vertical, horizontal, and two diagonal)
(iv) Flower with six petals - six lines of symmetry radiating from the center
(v) Robot/figure - one vertical line of symmetry through the middle
(vi) Regular hexagon - six lines of symmetry (three through opposite vertices, three through midpoints of opposite sides)
(vii) Pentagon - one vertical line of symmetry if regular
(viii) Scissors - one vertical line of symmetry through the handles and blades

Exam Tip: Regular polygons have lines of symmetry equal to their number of sides. For irregular shapes, count carefully - each line must divide the shape into two identical mirror images.

 

Question 10. State whether the following statements are true or false:
(i) A right-angled triangle can have at most two lines of symmetry
(ii) An isosceles triangle with more than one line of symmetry must be an equilateral triangle
(iii) A pentagon with one line of symmetry can be drawn.
(iv) A pentagon with more than one line of symmetry must be regular
(v) A hexagon with one line of symmetry can be drawn
(vi) A hexagon with more than one line of symmetry must be regular
Answer:
(i) False - A right-angled triangle can have at most one line of symmetry (only if it is an isosceles right-angled triangle). If it is an isosceles right triangle, there is one line of symmetry. Otherwise, there is no line of symmetry.

(ii) True - If an isosceles triangle has more than one line of symmetry, then it must be an equilateral triangle. This is because an equilateral triangle has three lines of symmetry, and a triangle cannot have exactly two lines of symmetry.

(iii) True - A pentagon with one line of symmetry can be constructed. The symmetry line passes through one vertex and the midpoint of the opposite side.

(iv) True - If a pentagon has more than one line of symmetry, it must be regular. A regular pentagon has five lines of symmetry, and an irregular pentagon cannot have more than one line of symmetry.

(v) True - A hexagon with one line of symmetry can be drawn. It does not need to be regular; it just needs one line along which it folds symmetrically.

(vi) True - If a hexagon has more than one line of symmetry, it must be regular. A regular hexagon has six lines of symmetry.

Exam Tip: Remember that a shape can only have two lines of symmetry if those lines are specific to that shape's geometry. For triangles, the maximum is three (equilateral). For most irregular shapes, additional symmetry lines force them to become regular polygons.

Exercise 17.4

 

Question 1. The total number of lines of symmetry of a scalene triangle is
(a) 1
(b) 2
(c) 3
(d) None of the options
Answer: (d) None of the options
In simple words: A scalene triangle has no lines of symmetry at all because all three sides and all three angles are different from each other.

Exam Tip: Remember that only triangles with equal sides (isosceles or equilateral) have symmetry lines. A scalene triangle, being completely asymmetrical, has zero lines of symmetry.

 

Question 2. The total number of lines of symmetry of an isosceles triangle is
(a) 1
(b) 2
(c) 3
(d) None of the options
Answer: (a) 1
In simple words: An isosceles triangle has exactly one line of symmetry. This line runs down the middle from the top point to the base, dividing the triangle into two matching halves.

Exam Tip: The single line of symmetry always passes through the vertex between the two equal sides and the midpoint of the base.

 

Question 3. An equilateral triangle is symmetrical about each of its
(a) altitudes
(b) median
(c) angle of bisectors
(d) All of the above
Answer: (d) All of the above
In simple words: In an equilateral triangle, the heights, centre lines, and angle dividers are all the same thing. So the shape is symmetrical when folded along any of these three lines.

Exam Tip: Equilateral triangles have a special property where altitudes, medians, and angle bisectors all coincide, creating three equal lines of symmetry.

 

Question 4. The total number of lines of symmetry of a square is
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (d) 4
In simple words: A square has four lines of symmetry - two that go through opposite corners, and two that go through the middle points of opposite sides.

Exam Tip: Always count both diagonal lines and the horizontal/vertical centre lines when identifying symmetry lines in a square.

 

Question 5. A rhombus is symmetrical about
(a) Each of its diagonals
(b) The line joining the mid-points of its opposite sides
(c) Perpendicular bisectors of each of its sides
(d) None of these
Answer: (a) Each of its diagonals
In simple words: A rhombus has exactly two lines of symmetry, and these are its two diagonals. When you fold the shape along either diagonal, the two halves match perfectly.

Exam Tip: The diagonals of a rhombus always intersect at right angles and serve as the only lines of symmetry.

 

Question 6. The number of lines of symmetry of a rectangle is
(a) 0
(b) 2
(c) 4
(d) 1
Answer: (b) 2
In simple words: A rectangle has two lines of symmetry - one goes through the centre horizontally and the other goes through the centre vertically. These two lines cut the rectangle into equal matching halves.

Exam Tip: Unlike a square, a rectangle does not have diagonal lines of symmetry because its sides are unequal in length.

 

Question 7. The number of lines of symmetry of a kite is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (b) 1
In simple words: A kite has just one line of symmetry. This line runs from the top point to the bottom point, dividing the kite into two identical halves on either side.

Exam Tip: The single line of symmetry in a kite always runs along its main diagonal, connecting the vertices where unequal sides meet.

 

Question 8. The number of lines of symmetry of a circle is
(a) 0
(b) 1
(c) 4
(d) Unlimited
Answer: (d) Unlimited
In simple words: A circle has endless lines of symmetry. Every single line passing through the centre divides it into two matching halves, so there are infinitely many such lines.

Exam Tip: Circles have infinite symmetry because every diameter creates a perfect fold line. This makes circles unique among common shapes.

 

Question 9. The number of lines of symmetry of a regular hexagon is
(a) 1
(b) 2
(c) 6
(d) 8
Answer: (c) 6
In simple words: A regular hexagon has six lines of symmetry. Three pass through opposite corner points, and three pass through the middle points of opposite sides.

Exam Tip: For any regular polygon, the number of lines of symmetry equals the number of sides it has.

 

Question 10. The number of lines of symmetry of an n - sided regular polygon is
(a) n
(b) 2n
(c) n/2
(d) None of these
Answer: (a) n
In simple words: For any regular polygon with n sides, the count of symmetry lines matches the side count. So if you have a shape with n sides, it will have exactly n lines of symmetry.

Exam Tip: This rule applies to all regular polygons - the number of symmetry lines always equals the number of sides.

 

Question 11. The number of lines of symmetry of the letter O of the English alphabet is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (c) 2
In simple words: The letter O has two lines of symmetry - one horizontal and one vertical - both running through its centre point.

Exam Tip: The letter O is circular in shape, so it has the same symmetry properties as an oval or ellipse, unlike other letters of the alphabet.

 

Question 12. The number of lines of symmetry of the letter Z of the English alphabet is
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (a) 0
In simple words: The letter Z has no lines of symmetry. No matter how you try to fold it, the two halves will never match perfectly.

Exam Tip: The Z-shape is asymmetrical by design, making it one of the few letters without any symmetry line.