Ch-Test of Mid-Point and Intercept Theorems Class 9 OP Malhotra ICSE Maths Solutions Ch-9. We Provide Step by Step Solutions / Answer of Mid-Point and Intercept Theorems OP Malhotra Maths. Visit official Website CISCE for detail information about ICSE Board Class-9 Mathematics.
Mid-Point and Intercept Theorems Class 9 OP Malhotra Ch-Test ICSE Maths Solutions Ch-9
| Board | ICSE |
| Publications | S Chand |
| Subject | Maths |
| Class | 9th |
| Chapter-9 | Mid-Point and Intercept Theorems |
| Writer | OP Malhotra |
| Ch-Test | Extra Practice Questions |
| Edition | 2026-2027 |
Ch-Test on Mid-Point and Intercept Theorems
Mid-Point and Intercept Theorems Class 9 OP Malhotra ICSE Maths Solutions Ch-9
Que-1: Use mid-segment theorem to name following parts of the given triangle.
(a) A mid-segment of ∆ABC
(b) A segment parallel to AC
(c) A segment that has the same length as BD
(d) A segment that has half the length of AC
(e) A segment that has twice the length of EC
Sol: In the given ∆ABC
AD = DB and BE = EC
∴ D and E are mid points of AB and BC respectively
∴ DE || AC and DE = 1/2 AC
(a) DE is mid segment of AABC
(b) DE is parallel to AC
(c) AD = BD
(d) DE is half of AC
(e) Twice of EC = BC (∵ BE = EC)
Que-2: Find each measure:
(a) NM (b) XZ (c) NZ (d) ∠LMN (e) ∠YXZ (f) XXLM
Sol: In the given figure,
∵ YL = LX, YM = MZ and XN = NZ
∴ L, M and N are the mid points of sides XY,
YZ and XZ respectively
∴ LM = 1/2 XZ, MN = 1/2 XY
XY = 10 cm, LM = 6 cm, ∠MNZ = 25°‘
(a) NM = 1/2 XY = 1/2 x 10 cm = 5 cm
(b) XZ = 2 x LM = 2 x 6 = 12 cm
(c) NZ = 1/2 x XZ = 1/2 x 12 = 6 cm
(d) ∠LMN = 25°
(∵ LM || XZ and MN is a transversal)
(Alternate angles)
(e) ∠YXZ = ∠MNZ = 25°
(corresponding angles)
(f) ∠XLM = ∠XNM
(opposite angles of a ||gm) = 180° – 25°
= 155°
Que-3: Find the value of n in each triangle.
Sol: In ∆ABC,
AL = LB and CM = MB
∴ LM || AC and LM = 1/2 AC
⇒ 32 = 1/2 x 4n
⇒ 2n = 32 32
⇒ n = 32/2 = 16 cm
∴ n = 16 cm
Que-4: Find the value of n in each triangle.
Sol: In ∆ABC,
AE = EC and BD = DC
∴ DE || AB and DE = 1/2 AB
⇒ 6n – 4n = +12
⇒ 2n = 12
n = 12/2 = 6
Que-5: In the figure, CG, EH and FJ are mid-segments of ∆ABD, ∆GCD and ∆GHE respectively. Find each measure:
(a) CG (b) EH (c) FJ (d) m∠DCG (e) m∠GHE (f) m∠FJH
Sol: In the given figure,
CG, EH and FJ are mid segments of ∆ABD, ∆GCD and ∆GHE respectively AB = 33 cm, ∠ABC = 57°
(a) CG = 1/2 AB
= 1/2 x 33 = 16.5 cm
(b) EH = 1/2 DC
= 1/2 x 1/2 DB
= 1/4 DB = 1/4 x 44 = 11 cm
(c) FJ = 1/2 GH = 1/2 x 1/2 GC
= 1/4 GC = 1/4 x 6.5 cm = 4.125 cm
(d) m∠DCG = ∠DBA
(corresponding angles)
= 57°
(e) m∠GHE = ∠GCD
(corresponding angles)
= 57°
(f) m∠FJH = 180° – ∠GHE
= 180° – 57° = 123°
Que-6: Prove that the perimeter of a mid-segment triangle is half the perimeter of the triangle.
Sol: In ∆ABC, D, E and F are the mid-points of sides BC, CA and AB respectively, forming mid segment ∆DEF
∵ D, E and F are the mid points of the sides
∴ DE = 1/2 AB, EF = 1/2 BC and DF = 1/2 AC
Now perimeter of ∆DEF = DE + EF + DF
= 1/2 AB + 1/2 BC + 1/2 CA
= 1/2(AB + BC + CA)
= Half perimeter of ∆ABC
Hence proved.
— : End of Mid-Point and Intercept Theorems 9 OP Malhotra Ch-Test ICSE Maths Step by step Solutions :–
Return to :– OP Malhotra S Chand Solutions for ICSE Class-9 Maths
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