Exercise 4.4 - Geometry
6th Maths : Term 1 Unit 4 : Questions with Answers & Solutions
Miscellaneous Practice Problems
1. Find the type of lines marked in thick lines (Parallel, intersecting or perpendicular).
Answer:
(i) Parallel lines
(ii) Parallel lines
(iii) Parallel & Perpendicular lines
(iv) Intersecting lines.
(ii) Parallel lines
(iii) Parallel & Perpendicular lines
(iv) Intersecting lines.
2. Find the parallel and intersecting line segments in the picture given below.
3. Name the following angles as shown in the figure.
Answer:
(i) ∠1 = ∠CBD (or) ∠DBC
(ii) ∠2 = ∠DBE (or) ∠EBD
(iii) ∠3 = ∠EBA (or) ∠ABE
(iv) ∠1 + ∠2 = ∠CBE (or) ∠EBC
(v) ∠2 + ∠3 = ∠DBA (or) ∠ABD
(vi) ∠1 + ∠2 + ∠3 = ∠ABC (or) ∠CBA
(ii) ∠2 = ∠DBE (or) ∠EBD
(iii) ∠3 = ∠EBA (or) ∠ABE
(iv) ∠1 + ∠2 = ∠CBE (or) ∠EBC
(v) ∠2 + ∠3 = ∠DBA (or) ∠ABD
(vi) ∠1 + ∠2 + ∠3 = ∠ABC (or) ∠CBA
4. Measure the angles of the given figures using protractor and identify the type of angle as acute, obtuse, right or straight.
Answer:
(i) Right angle
(ii) Acute angle
(iii) Straight line
(iv) Obtuse angle
(ii) Acute angle
(iii) Straight line
(iv) Obtuse angle
5. Draw the following angles using the protractor.
(i) 45º (ii) 120º (iii) 65º (iv) 135º (v) 0º (vi) 180º (vii) 38º (viii) 90º
6. From the figures given below, classify the following pairs of angles into complementary and non-complementary.
Answer:
Complementary – (i) & (v)
Non−complementary − (ii), (iii) & (iv)
Non−complementary − (ii), (iii) & (iv)
7. From the figures given below, classify the following pairs of angles into supplementary and non-supplementary.
Answer:
Supplementary − (ii) & (iv)
Non−Supplementary − (i), (iii)
Non−Supplementary − (i), (iii)
8. From the figure (i) name a pair of complementary angles (ii) name a pair of supplementary angles
Answer:
(i) Complementary angles: ∠FAE & ∠EAD
(ii) Supplementary angles:
(a) ∠FAD & ∠DAC
(b) ∠BAF & ∠FAE
(c) ∠EAD & ∠DAB
(d) ∠BAC & ∠CAE
(ii) Supplementary angles:
(a) ∠FAD & ∠DAC
(b) ∠BAF & ∠FAE
(c) ∠EAD & ∠DAB
(d) ∠BAC & ∠CAE
9. Find the complementary angle of
(i) 30º (ii) 26º (iii) 85º (iv) 0º (v) 90º
Solution: Complementary angle (90°− θ)
(i) 90° − 30° = 60°
(ii) 90° − 26° = 64° (Note: Source text says 35 & 65, but 90-26=64)
(iii) 90° − 85° = 5°
(iv) 90° − 0° = 90°
(v) 90° − 90° = 0°
(ii) 90° − 26° = 64° (Note: Source text says 35 & 65, but 90-26=64)
(iii) 90° − 85° = 5°
(iv) 90° − 0° = 90°
(v) 90° − 90° = 0°
10. Find the supplementary angle of
(i) 70º (ii) 35º (iii) 165º (iv) 90º (v) 0º (vi) 180º (vii) 95º
Solution: Supplementary angle (180° − θ°)
(i) 180° − 70° = 110°
(ii) 180° − 35° = 145°
(iii) 180° − 165° = 15°
(iv) 180° − 90° = 90°
(v) 180°− 0° = 180°
(vi) 180° − 180° = 0°
(vii) 180° − 95° = 85°
(ii) 180° − 35° = 145°
(iii) 180° − 165° = 15°
(iv) 180° − 90° = 90°
(v) 180°− 0° = 180°
(vi) 180° − 180° = 0°
(vii) 180° − 95° = 85°
Challenging Problems
11. Think and write an object having
● Parallel lines (1) __________ (2) __________ (3) __________
● Perpendicular lines (1) __________ (2) __________ (3) __________
● Intersecting lines (1) __________ (2) __________ (3) __________
Answer:
Parallel lines: (1) Railway Track (2) Edges of scale (3) Legs of table
Perpendicular lines: (1) Cross bars of windows (2) Adjacent sides of text book (3) Adjacent sides of Black board
Intersecting lines: (1) Ladder (2) Blades of scissor (3) Cross bars of windows
Perpendicular lines: (1) Cross bars of windows (2) Adjacent sides of text book (3) Adjacent sides of Black board
Intersecting lines: (1) Ladder (2) Blades of scissor (3) Cross bars of windows
12. Which angle is equal to twice its complement?
Answer: 60°
13. Which angle is equal to two-third of its supplement?
Answer: 72°
14. Given two angles are supplementary and one angle is 20º more than other. Find the two angles.
Answer: The two angles are 80° & 100°
15. Two complementary angles are in ratio 7:2. Find the angles.
Answer: Two angles are 70° & 20°
16. Two supplementary angles are in ratio 5:4. Find the angles.
Answer: The angles are 100° & 80°
EUCLID (325 BC – 265 BC)
He was a Greek Mathematician who founded plane geometry through his postulates in a set of 13 books called "ELEMENTS". His work influenced the world’s understanding of geometry for generations.