Page 312 - ICSE Math 7

Exercise 15.2 Exercise 16.2
1. (a) Corresponding angles (b) Vertically opposite angles 1. (a), (c) and (d)
(c) Corresponding angles (d) Co-interior angles 2. (a) 6 cm (b) 17 cm (c) 25 cm (d) 9 cm
(e) Vertically opposite angles (f) Alternate exterior angles 3. 96 cm 4. 5 m 5. 13 m 6. 50 km 7. 11 cm
(g) Alternate interior angles (h) Linear pair 8. (b) 9. 13 cm
(i) Co-interior angles Mental Maths
2. (a) 55° (b) 140° (c) 60° 1. (a) (iii) (b) (ii) (c) (ii) (d) (iii) (e) (ii)
3. x = 135°; y = 40°; z = 140° 2. (a) True (b) False (c) True (d) True
4. (a) x = 55°; y = 110° (b) x = 62°; y = 68° 3. (a) median (b) altitude (c) point; centroid
(c) x = 60°; y = 58° (d) x = 90°, y = 120°; z = 60° (d) concurrent; orthocentre (e) hypotenuse
(e) x = 125°; y = 55°; z = 55° (f) x = 50°; y = 150°
Practice Time
Mental Maths 1. 30° and 60° 2. 37 m 3. 5 cm each 4. 360°
1. (a) False (b) True (c) False (d) False (e) False 5. 36°; 72°; 72°
(f) True 6. (a) x = 75°; y = 105° (b) x = 35°; y = 95°
2. (a) 30° (b) 10° (c) 60° (d) equal (e) linear pair 7. 17 m 8. 36°; 90° 9. 100 m 10. 8 inches
(f) obtuse
Think Smart
Practice Time 1. 90°; 67.5°; 22.5° 2. x = 95°; y = 130°
1. (a) 22° (b) 45° (c) 95° 3. 96°; 48° : 36° 4. PQ = 17 cm and RS = 5 cm
2. ∠2 = 115°; ∠3 = 65°; ∠4 = 115°; ∠5 = 65°; ∠6 = 115°;
∠7 = 65°; ∠8 = 115° Chapter 17
3. (a) Not parallel (b) Parallel (c) Parallel
4. (a) 20° (b) 130° 5. 60°; 80° 6. 20°; 120° 7. 60° Exercise
8. (a) x = 115°; y = 70°; z = 70° 1. DDEF ≅ DPQR (by ASA)
(b) x = 45°; y = 55°; z = 80° 2. (a) Yes, SSS (b) No (c) No (d) Yes, SAS
(c) x = 60°; y = 56°; z = 124° (e) Yes; SAS (f) No
3. (a) PQ ↔ XY, QR ↔ YZ, RP ↔ ZX
Think Smart ∠ P ↔ ∠X, ∠Q ↔ ∠Y, ∠R ↔ ∠Z
1. 24 2. 334° 13' 42" (b) OP ↔ FU, PT ↔ UG, OT ↔ FG
3. (a) 90° (b) 180° < A < 360° (c) 125° (d) 180° – ∠Q ∠O ↔ ∠F, ∠P ↔ ∠U, ∠T ↔ ∠G

Chapter 16 4. AD = BC (given)
ED = FC (distance between parallel lines)
Exercise 16.1 ∠AED = ∠BFC (each 90°)
1. (a) No (b) Yes (c) Yes ∴ DAED ≅ DBFC (by RHS)
2. (a) ∠P = 40°; obtuse-angled triangle AE = BF (CPCT)
(b) ∠C = 80°; acute-angled triangle 5. (a) B AB = AC (given)
(c) ∠C = 20°; acute-angled triangle BD = DC (median)
(d) ∠Q = ∠R = 20°; obtuse-angled triangle AD = AD (common)
(e) ∠A = 60°; ∠C = 40°; acute-angled triangle A 1 D 2 C ∴ DABD ≅ DACD (By SSS)

3. 90°, 30°; 60°; right-angled triangle ∠1 = ∠2 (CPCT)
4. (a) x =18°; ∠A = 90°; ∠B =54°; ∠C = 36° ∠1 + ∠2 = 180° (Linear pair)
(b) x = 60°; ∠P = ∠Q = ∠R = 60° 2∠1 = 180°, ∠1 = 90°
(c) x = 75°; ∠M = 85°; ∠N = 65° (b) A ∠P = ∠Q = 90°, ∠B = ∠C = 60°,
(d) x = 18; ∠Q = 36°, ∠R = 54° P Q BC = BC (common)
5. 50°; 60° DBCP ≅ DCBQ (by AAS)
6. (a) x = 10°; y = 105° (b) x = 115°; y = 115° B C Hence BQ = CP (CPCT)
(c) x = 92.5° (d) x = 122° 6. DA = CB (given), AX = BY ⇒ AX + XY = XY + BY
7. (a) Isosceles (b) Equilateral (c) Isosceles ⇒ AY = BX, ∠A = ∠B (each 90°)
8. 40°; 40°; 100° DDAY ≅ DCBX (by SAS)

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