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Byju's Answer
Standard IX
Mathematics
Trigonometric Ratios
ABC is a tria...
Question
ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallels to BC intersect AC at D. Show that CM=MA=
1
2
A
B
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Solution
To show :
C
M
=
M
A
=
1
2
A
B
In
△
A
M
D
and
△
C
M
D
A
D
=
D
C
(
D
is midpoint)
∠
A
D
M
=
∠
C
D
M
D
M
=
D
M
(common)
△
A
M
D
=
≅
△
C
M
D
(
S
A
S
congruence rule )
∴
A
M
=
C
M
(
C
P
C
T
)
−
−
−
−
−
−
−
−
−
−
−
−
−
(
1
)
A
M
=
1
2
A
B
(
M
i
s
m
i
d
p
o
i
n
t
)
−
−
−
−
−
−
−
−
−
−
(
2
)
from eq
(
1
)
and
(
2
)
C
M
=
A
M
=
1
2
A
B
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Similar questions
Q.
ABC is a triangle right angled at C. A line through the mid point M of hypotenuse AB and parallel to BC intersect AC at D .Show that :
C
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Q.
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[4 MARKS]
Q.
Triangle ABC is right angled at
C
. A line through the mid-point
M
of hypotenuse
A
B
and parallel to
B
C
, intersects AC at D.
Show that:
C
M
=
M
A
=
1
2
A
B
Q.
A
B
C
is a triangle right angled at
C
.
A
line through the mid-point
M
of hypotenuse
A
B
and parallel to
B
C
intersects
A
C
at
D
.
Show that
(
i
)
D
is the mid-point of
A
C
(
i
i
)
M
D
⊥
A
C
(
i
i
i
)
C
M
=
M
A
=
1
2
A
B
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