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CHAPTER 5: EUCLID’S GEOMETRY
Q1 Prove that any line segment has one and only one mid-point.
Q2 Prove that an equilateral can be constructed on any given line segment.
Q3 C is the mid-point of segment AB and P is the mid-point of segment AC, prove that CP=¼AB
Q4 Prove that two distinct lines cannot have more than one point in common.
Q5 In the figure BX = ½AB and BY= ½BC2 if AB=BC show that BX=BY
Q6 In given figure we have CDAB (1=2=90o) 3 = 4 Show that CDE=CDF
Q7 If B is a point between A and C and all three points lie in a line show that AB+BC=AC
Mathematics Assignments Class IX TERM I 2017 – 18
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CHAPTER 6: LINES AND ANGLES
Q1 Write complement and supplement of (90o–ao)
Q2 If angles of a triangle are in the ratio of 3:4:5 find measure of each angle.
Q3 In ABC if 24A = 8B = 3C then find A, B and C
Q4 If one angle of a triangle is greater than sum of other two then show that triangle is an obtuse angled triangle.
Q5 In PQR the internal bisectors of Q & R meet at I. Prove that
a) IQR + IRQ = 90 – ½PQR
b) QIR = 90 + ½PQR
Q6 S is a point in the interior of PQR prove that SQ + SR < PQ + PR
Q7 Prove that bisectors of angles of a linear pair are right angles.
Q8 ABC is right angled at A. L is a point on BC such that AL BC. Prove that BAL = ACB
Q9 If two parallel lines are intersected by a transversal prove that bisectors of interior angles on same side of transversal intersect each other at right angles.
Q10 Show that sum of interior angles of a triangle is 180o.
Q11 Find the value of ‘x’ and ‘y’
a)
b)
Mathematics Assignments Class IX TERM I 2017– 18
–2–
Mathematics Assignments Class IX TERM I 2016 – 17
c)
HOTS
Q12 In given figure PS bisects TPQ. PQR is isosceles. Prove that PS || RQ
Q13 In given figure AB = AC. D is a point on AC and E is a point on AB such that AD=ED=EC=BC.
Prove that AED = BCE
–3–
CHAPTER – I: NUMBER SYSTEMS
Q1 Write following rational numbers in decimal form
a) 13
4
b)
8
27
c)
125
7
d)
11
2
Q2 Express in the form of
q
p
a) 10.10 b) .050505... c) . 725 d) . 13 e) . 67
Q3 Insert two rational and two irrational numbers between
a) 2.25 and 2.26 b) 2 and 3 c) 4
3and
7
5 d)
3
2and 0
Q4 In the following equations find which of the variables x, y, z etc represent rational or irrational numbers
a) 4
172 x b) y2=3 c) z3=27 d) a2=0.4
Q5 Simplify
a)
3
2
3
1
3
1
)64()64()64( b) 4041
3940
33
33
c)
64
53
510
432
5
3
5
7
3
4
5
3
5
1
4
1
3
1
2
1
Q6 Rationalise
a) 534
534
b)
1429
25
c)
1156
15
d)
532
1
532
1
Q7 Find the values of ‘a’ and ‘b’
a) 323223
6ba
b)
5
15
15
15
15ba
Q8 If
223
1,
223
1
yx find (a) x2+y2 b) x3+y3
Q9 Prove that
a) 525
1
56
1
67
1
78
1
83
1
b) 298
1
43
1
32
1
21
1
Q10 Simplify
a) 1878420 b) 1752863
c) 2352 d) 73285
e)
72
2
35
3
15
3
22
2
176
Q11 If
32
1
x find the value of x3–2x2–7x+5
Q12 Find ‘x’ if
16
81
2
3
3
22
xx
Q13 If a=2 and b=3 find (a) (ab + ba)–1 (b) (aa + bb)–1
Q14 Find ‘p’ if (a) 5)2()5( 54 pp (b) p243 )2()2(
Mathematics Assignments Class IX TERM I 2017 – 18
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Do all the assignments in a separate register.
