CONSTRUCTIONS
7 cm
A′B
AB
=
BC′
BC
=
A′C′
AC
=
7
5
B
A
C
6 cm
Rough Figure
S
R
P
Q
V
W
T
U
C
B
7 cm
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Ex-13.1 (Q.3)
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A
5 cm
6 cm
B1
B2
B3
B4
B5
B6
B7
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A'
C'
Draw seg BC = 7cm
B as centre, r = 6cm,
draw an arc
C as centre and r = 5cm,
cut the previous arc
mark point A
Draw AB and AC
Draw ray BX
X
Considering any suitable radius, draw 7 arcs on ray BX
Draw B5C
B5 as centre and any suitable radius, draw an arc intersecting BX and B5C at points P & Q respectively
B7 as centre and with the same radius, draw an arc intersecting BX at point R
Now, consider radius = PQ
R as centre, cut an arc and mark that point S
Draw B7S intersecting BC at C'
C as centre and any suitable radius, draw an arc intersecting BC and AC at points T & U respectively
C' as centre and with the same radius, draw an arc intersecting BC at point V
Now consider radius = TU
V as centre, cut an arc and mark that point W
Draw C'W intersecting AB at A'
A′
C′
5 cm
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Any point on the line as centre and radius = 7 cm, draw an arc
C as the centre and same radius, draw another arc
C
B
7 cm
A
5 cm
6 cm
B1
B2
B3
B4
B5
B6
B7
A'
C'
X
Justification :
∴
A′C′ ║ AC
[by construction]
ΔA′BC′ ~ ΔABC
[AA Similarity]
A′B
AB
=
BC′
BC
=
A′C′
AC
[corresponding sides of
similar triangles]
But,
BC′
BC
=
BB5
=
7
5
∴
BC′
BC
=
7
5
∴
A′B
AB
=
BC′
BC
=
A′C′
AC
=
7
5
[since ΔBB5C ~ΔBB7Cl]