Term 1 · Class 6 Maths · Chapter 4

Samacheer Class 6 Maths - Geometry

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Chapter-wise textbook exercise answers for Geometry with validation-aware solutions.

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Q.1Fill in the blanks. (i) A line through two endpoints ‘A’ and ‘B’ is denoted by ______ (ii) Aline segment from point ‘B’ to point ‘A’ is denoted by ______ (iii) A ray has ______ endpoint(s).v
Solution

(i) \(\overleftrightarrow { AB }\)
(ii) \(\bar { BA } \)
(iii) one
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1

Answer:

(i) \(\overleftrightarrow { AB }\)
(ii) \(\bar { BA } \)
(iii) one
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1

Q.2Construct a line segment using a ruler and compass. (1) \(\overline { AB } \) = 7.5 cm (2) \(\overline { CD } \) = 3.6 cm (3) \(\overline { QR } \) = 10 cmv
Solution

(1)
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1 3
(i) Draw line 1 and mark a point A on it.
(ii) Measure 7.5 cm using a compass, placing the pointer at ‘O’ and the pencil pointer at 7.5 cm.
(iii) Place the pointer of the compass at A then draw a small arc on the line 1 with the pencil pointer. It cuts line 1 at a point and name that point as B.
(iv) Now \(\overline { AB } \) is the required line segment of length 7.5 cm.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1
(2)
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1 4
(i) Draw a line 1 and mark a point C on it.
(ii) Measure 3.6 cm using a compass, placing the pointer at O and the pencil pointer at 3.6 cm.
(iii) Place the pointer of the compass at C then draw a small arc on the line 1 with the pencil pointer. It cuts line 1 at a point and names the point as D.
(iv) Now \(\overline { CD } \) is the required line segment of length 3.6 cm.
(3)
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1 5
(i) Draw a line 1 and mark a point Q on it.
(ii) Measure 10 cm using compass placing the pointer at O and the pencil pointer at 10 cm.
(iii) Place the pointer of the compass at Q then draw a small arc on the line 1 with the pencil pointer. It cuts the line 1 at a point and name that point as R.
(iv) Now \(\overline { QR }\) is the required line segment of length 10 cm.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1

Answer:

(1)
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1 3
(i) Draw line 1 and mark a point A on it.
(ii) Measure 7.5 cm using a compass, placing the pointer at ‘O’ and the pencil pointer at 7.5 cm.
(iii) Place the pointer of the compass at A then draw a small arc on the line 1 with the pencil pointer. It cuts line 1 at a point and name that point as B.
(iv) Now \(\overline { AB } \) is the required line segment of length 7.5 cm.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1
(2)
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1 4
(i) Draw a line 1 and mark a point C on it.
(ii) Measure 3.6 cm using a compass, placing the pointer at O and the pencil pointer at 3.6 cm.
(iii) Place the pointer of the compass at C then draw a small arc on the line 1 with the pencil pointer. It cuts line 1 at a point and names the point as D.
(iv) Now \(\overline { CD } \) is the required line segment of length 3.6 cm.
(3)
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1 5
(i) Draw a line 1 and mark a point Q on it.
(ii) Measure 10 cm using compass placing the pointer at O and the pencil pointer at 10 cm.
(iii) Place the pointer of the compass at Q then draw a small arc on the line 1 with the pencil pointer. It cuts the line 1 at a point and name that point as R.
(iv) Now \(\overline { QR }\) is the required line segment of length 10 cm.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1

Q.3A line is denoted as __________v
  1. A. AB
  2. B. \(\overrightarrow{AB}\)
  3. C. \(\overleftrightarrow {AB} \)
  4. D. \(\overline { AB }\)
Solution

(c) \(\overleftrightarrow {AB} \)
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1
Posted in Class 6 on January 22, 2025 January 23, 2025
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Answer:

(c) \(\overleftrightarrow {AB} \)
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.1
Posted in Class 6 on January 22, 2025 January 23, 2025
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Q.4Say True or False. (i) 20° and 70° are complementary. (ii) 88° and 12° are complementary. (iii) 80° and 180° are supplementary. (iv) 0° and 180° are supplementary.v
Solution

(i) True
Hint: 20°+ 70° = 90°
(ii) False
Hint: 88° + 180° = 260° ≠ 1
(iii) False
Hint: 80° + 180° = 260° ≠ 1
(iv) True
Hint: 0° + 180° = 180°

Answer:

(i) True
Hint: 20°+ 70° = 90°
(ii) False
Hint: 88° + 180° = 260° ≠ 1
(iii) False
Hint: 80° + 180° = 260° ≠ 1
(iv) True
Hint: 0° + 180° = 180°

Q.5Draw and label each of the angles. (i) ∠NAS = 90°n (ii) ∠BIG = 35° (iii) ∠SMC = 145°v
Solution

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.2 14
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.2

Answer:

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.2 14
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.2

Q.6In this figure, ∠AYZ = 45. If point ‘A’ is shifted to point ‘B’ along the ray, then the measure of ∠BYZ is Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.2 19v
  1. A. more than 45°
  2. B. 45°
  3. C. less than 45°
  4. D. 90°
Solution

(b) 45°
Posted in Class 6 on January 22, 2025 January 23, 2025
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Answer:

(b) 45°
Posted in Class 6 on January 22, 2025 January 23, 2025
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Q.7Draw any line and mark any 3 points that are collinear.v
Solution

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3 2

Answer:

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3 2

Q.8Draw any line and mark any 4 points that are not collinear.v
Solution

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3 3
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3

Answer:

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3 3
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3

Q.9Draw any 3 lines to have a point of concurrency.v
Solution

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3 4
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3

Answer:

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3 4
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3

Q.10Draw any 3 lines that are not concurrent. Find the number of points of intersection.v
Solution

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3 5
Number of points of intersection = 3
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3
Objective Type Questions
Observe the Diagram and give answers
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3 6

Answer:

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3 5
Number of points of intersection = 3
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3
Objective Type Questions
Observe the Diagram and give answers
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3 6

Q.11A set of collinear points in the figure arev
  1. A. A, B, C
  2. B. A, F, C
  3. C. B, C, D
  4. D. A, C, D
Solution

(b) A, F, C
Hint: Collinear points are points on a line.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3

Answer:

(b) A, F, C
Hint: Collinear points are points on a line.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3

Q.12A point of concurrency in the figure is ______v
  1. A. E
  2. B. F
  3. C. G
  4. D. H
Solution

(b) F
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3
Posted in Class 6 on January 22, 2025 January 23, 2025
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Answer:

(b) F
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.3
Posted in Class 6 on January 22, 2025 January 23, 2025
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Q.13Find the type of lines marked in thick lines (Parallel, intersecting or perpendicular) Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4 1v
Solution

(i) Parallel lines
(ii) Parallel lines
(iii) Parallel and Perpendicular lines
(iv) Intersecting lines
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4

Answer:

(i) Parallel lines
(ii) Parallel lines
(iii) Parallel and Perpendicular lines
(iv) Intersecting lines
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4

Q.14Find the complementary angle of (i) 30° (ii) 26° (iii) 85° (iv) 0° (v) 90°v
Solution

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4 9

Answer:

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4 9

Q.15Find the supplementary angle of (i) 70° (ii) 35° (iii) 165° (iv) 90° (v) 0° (vi) 180° (vii) 95°v
Solution

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4 10
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4
Challenging Problems

Answer:

Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4 10
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4
Challenging Problems

Q.16Think and write an object having (i) Parallel lines (1) ……….. (2) ………. (3) ……….. (ii) Perpendicular lines (1) ……… (2) ……… (3) ……….. (iii) Intersecting lines (1) ……….. (2) ………. (3) ……….v
Solution

(i) Legs of the table, railway tracks, edges of the scale
(ii) Adjacent sides of a Board, Crossbars of windows, Adjacent sides of the textbook
(iii) Crossbars of windows, Ladder, blades of a scissor.

Answer:

(i) Legs of the table, railway tracks, edges of the scale
(ii) Adjacent sides of a Board, Crossbars of windows, Adjacent sides of the textbook
(iii) Crossbars of windows, Ladder, blades of a scissor.

Q.17Which angle is equal to twice its complement.v
Solution

Let the angle be x
According to the problem, x = 2 × (90 – x)
x = 180 – 2x
x + 2x = 180
3x = 180
x = \(\frac{180}{3}\)
x = 60
∴ The angle is 60°
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4

Answer:

Let the angle be x
According to the problem, x = 2 × (90 – x)
x = 180 – 2x
x + 2x = 180
3x = 180
x = \(\frac{180}{3}\)
x = 60
∴ The angle is 60°
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4

Q.18Which angle is equal to two-thirds of its supplement.v
Solution

Let the angle be x
According to the problem,
x = \(\frac{2}{3}\) × (180° – x)
3x = 2(180 – x)
3x = 360 – 2x
3x + 2x = 360°
5x = 360°
x = \(\frac{360°}{5}\)
x = 72°
∴ The angle is 72°

Answer:

Let the angle be x
According to the problem,
x = \(\frac{2}{3}\) × (180° – x)
3x = 2(180 – x)
3x = 360 – 2x
3x + 2x = 360°
5x = 360°
x = \(\frac{360°}{5}\)
x = 72°
∴ The angle is 72°

Q.19Given two angles are supplementary and one angle is 20° more than the other. Find the two angles.v
Solution

Let the angles be x and x + 20°
According to the problem,
x + x + 20 = 180°
2x + 20° = 180°
2x = 180° – 20°
2x = 160°
x = \(\frac{160°}{2}\)
x = 80°
x + 20 = 80° + 20°
= 100°
∴ The two angles are 80° and 100°
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4

Answer:

Let the angles be x and x + 20°
According to the problem,
x + x + 20 = 180°
2x + 20° = 180°
2x = 180° – 20°
2x = 160°
x = \(\frac{160°}{2}\)
x = 80°
x + 20 = 80° + 20°
= 100°
∴ The two angles are 80° and 100°
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4

Q.20Two complementary angles are in ratio 7 : 2. Find the angles.v
Solution

Let the angles be 7x, 2x
According to the problem,
7x + 2x = 90
9x = 90
x = \(\frac{90}{9}\)
x = 10
7x = 7 × 10
= 70
2x = 2 × 10
= 20
∴ Two angles are 70° and 20°

Answer:

Let the angles be 7x, 2x
According to the problem,
7x + 2x = 90
9x = 90
x = \(\frac{90}{9}\)
x = 10
7x = 7 × 10
= 70
2x = 2 × 10
= 20
∴ Two angles are 70° and 20°

Q.21Two supplementary angles are in ratio 5 : 4. Find the angles.v
Solution

Total of two supplementary angles = 180°
Given they are in the ratio 5 : 4
Dividing total angles to 5 + 4 = 9 equal parts.
One angle \(=\frac{5}{9} \times 180=100^{\circ}\)
Another angle \(=\frac{4}{9} \times 180=80^{\circ}\)
Two angles are 100° and 80°.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4
Posted in Class 6 on January 22, 2025 January 23, 2025
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Answer:

Total of two supplementary angles = 180°
Given they are in the ratio 5 : 4
Dividing total angles to 5 + 4 = 9 equal parts.
One angle \(=\frac{5}{9} \times 180=100^{\circ}\)
Another angle \(=\frac{4}{9} \times 180=80^{\circ}\)
Two angles are 100° and 80°.
Samacheer Kalvi 6th Maths Guide Term 1 Chapter 4 Geometry Ex 4.4
Posted in Class 6 on January 22, 2025 January 23, 2025
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