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DELHI PUBLIC SCHOOLBOKARO STEEL CITY
ASSIGNMENT FOR THE SESSION 2011-2012
Class: IX Subject : Mathematics Assignment No. 2
Co-ordinate geometry
1. Name the quadrants in which the following points liea) (2,
-3) b) (-7, -4) c) (-5, 1)
2. On which axis do these points lie?
a) (-4, 0) b) (0, 6) c) (0, -1)
3. Plot the following points on Cartesian plane
a) A (4, 7) b) B (3, -5) c) C (9, 0)
Introduction to Euclids geometry
1. Prove that two lines which are both parallel to the same line
are parallel to each other.2. If lines AB, AC, AD and AE are all
parallel to the same line l, then Show that the points A, B,
C, D and E are collinear.
Lines and angles
1. If a ray stands on a line, prove that the sum of the angle
bisectors of the adjacent angles soformed is 90
0.
2. Ray OC is perpendicular to the line AB at O. Another ray OD
is lying between rays OB andOC. Prove that COD = )BODAOD(
2
1
3. Given o78BAC = and BA is produced to D. If ray AE bisects
angle CAD, then find angle BAEand reflex angle DAE
4. If each angle of a triangle is less than the sum of the other
two, then show that the triangleis an acute angled triangle.
5. In PQR , If PM is perpendicular to QR and PN is the bisector
of P , then prove that)CB(
2
1MPN = .
6. If in a quadrilateral ABCD, the bisectors of A and D
intersect at point P, then prove that2 CBAPD +=
7. If AB is parallel to CD and P is a point between them, prove
that.360CDPBDPABP 0=++
Triangles
1. If ABC and DBC are isosceles triangles on the same base BC,
then show that the linejoining AD bisectsthe common base at right
angles.
2. If ABCD is a square and P is a point inside it such that
PB=PD, then prove that C PA is a
straight line.
3. If ABC is an equilateral triangle, P and Q are points on BC
and AB such that PQ is parallel to
AC and AC is produced to R such that CR=BP, then prove that QR
bisects PC.
4. If the bisector of the vertical angle of a triangle bisects
the base, then prove that it is anisosceles triangle.
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5. If ABCD is a square in which M is the midpoint of AB , PQ
which is perpendicular to CM meetsAD at P and CB produced at Q
,then prove that AP=BQ and CP=AB+PA .
6. If in ABC, D is a point on AC such that AB=AD, then prove
that BC>CD.
7. Prove that the line segment joining the midpoints of the
diagonals of a trapezium is parallelto each of the parallel sides
and is equal to half the difference between the lengths of the
twoparallel sides.
Herons Formula
1 Find the area of a triangle whose two sides are 60cm,100cmand
the perimeter is 300cm2 A field is in the shape of a trapezium
whose parallel sides are 25m and 10m. The non-
parallel sides are 14cm and 13cm. Find the area of the
field.
3 A farmer has a triangular field with sides 240m, 200m and
360m, where he grew wheat. Inanother triangular field with sides
240m, 320m and 400m adjacent to the previous field, hewanted to
grow potatoes and onions. He divided the field into two parts by
joining the mid
point of the longest side to the opposite vertex and grew
potatoes in one part and onions inthe other part. How much area (in
hectares) has been used for wheat, potatoes and onions?
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