Page 313 - ICSE Math 7

7. ∠A = ∠C (given); ∠ABM = ∠CBM (given) 2. (a) 3 (b) 1 (c) infinite (d) 0 (e) 1
BM = BM (common); DABM ≅ DCBM (by AAS) 3. Vertical–A, H, O; Horizontal–B, E, O
∠BMA = ∠BMC (CPCT)
⇒ ∠BMA = ∠BMC = 180° (Linear pair)
⇒ 2 ∠BMA = 180 4. (a) (b)
⇒ 2∠BMA = 90°, hence BM ⊥ AC scalene triangle
8. OP = OQ (midpoint), ∠A = ∠B (given) isosceles triangle
∠AOP = ∠BOQ (vertically opposite)
∴ DPAO ≅ DQBO (by AAS)
9. OD = OS (given), ∠K = ∠A (given) (c) not possible (d)
∠KOD = ∠AOS (vertically opposite)
∴ DKOD = DAOS (by AAS) equilateral triangle
10. ∠P = ∠T, PR = TI(CPCT) 5. no line of symmetry
PQ = TS (CPCT) ⇒ 2PA = 2TB ⇒ PA = TB 6. 3 7. Rhombus or rectangle 8. Trapezium
∴ DPAR ≅ DTBI (by SAS)
Hence, RA = IB (CPCT) Exercise 18.2
1. (a) (10, 10) (b) (–8, 7) (c) (7, –6) (d) (–3, –9)
Mental Maths (e) (–5, 0) 2. (a) (0, –5) (b) (–7, 10) (c) (3, 5)
1. (a) (iii) (b) (ii) (c) (iii) (d) (iv) (e) (i)
2. (a) True (b) False (c) True (d) False (e) True (d) (–4, –6) (e) (8, –9) 3. (a) (–5, –4)
3. (a) RT (b) hypotenuse (c) equal (d) ASA (b) (3, 1) (c) (–2, 8) (d) (12, –9) (e) (0, 0)
(e) congruent, SSS Y
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Practice Time 3
1. (a) Yes, ASA congruency criterion (b) ∠MPO (c) Yes 2 Q P
2. (a) AD = CF ⇒ AD + DC = DC + CF ⇒ AC = DF 1 R
CB = DE (given), ∠C = ∠D (each 90 °) 4. X' O S X
∴ DACB ≅ DFDE (by SAS) –4 –3 –2 –1 1 2 3 4
⇒ ∠A = ∠F (CPCT) which are alternate angles –1 R' S'
hence AB || EF –2 Q' P'
(b) AB = EF (CPCT) –3
3. (a) AB = AC and PB = PC (given) –4 Y'
AP = AP (common)
DAPB ≅ DAPC (by SSS) 4 Y
(b) ∠APB = ∠APC (CPCT) B' B
4. (a) FA = CT and FT = CA C' 3 2
(opposite sides of a parallelogram) C
AT = AT (common) X' A 1 O A' X
∴ DFAT ≅ DCTA (by SSS) 5. –4 –3 –2 –1 1 2 3 4
(b) ∠ATF = ∠TAC (CPCT) –1
5. (a) AB = AC, AD = AD, ∠ADB = ∠ADC –2
(b) Yes, DADB ≅ DADC (By RHS) –3
(c) Yes, BD = CD (CPCT) –4 Y'
(d) Yes, ∠BAD = ∠CAD (CPCT)
6. Raman should buy triangular glasses (b) and (d) since 4 Y
they are congruent by SSS criterion. A
3
Chapter 18 2 B'
Exercise 18.1 X' 1 X
6. O
–4 –3 –2 –1 1 2 3 4 5
–1
1. (a) (b) (c) –2 B
–3
–4 A'
(d) not possible Y'

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