5
You visited us
5
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard IX
Mathematics
SAS Criteria for Congruency
ABC is a tria...
Question
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
M
=
M
A
=
1
2
A
B
Open in App
Solution
I
n
Δ
A
B
C
M
is the midpoint of
A
B
and
M
D
∥
B
C
therefore
D
is the midpoint of
A
C
[line drawn through midpoint of one side of a triangle parallel to another side, bisect the third side]
⇒
A
D
=
D
C
⟶
(
1
)
also,
∠
A
D
M
=
∠
C
D
M
=
90
o
(
c
o
r
r
e
s
p
o
n
d
i
n
g
a
n
g
l
e
)
I
n
Δ
A
D
M
a
n
d
Δ
C
D
M
A
D
=
C
D
(
f
r
o
m
(
1
)
)
∠
A
D
M
=
∠
C
D
M
=
90
o
D
M
=
D
M
(
c
o
m
m
o
n
)
∴
Δ
A
D
M
≅
Δ
C
D
M
(
S
A
S
)
∴
A
M
=
C
M
(
C
P
C
T
)
∵
A
M
=
1
2
A
B
(
M
i
s
t
h
e
m
i
d
p
o
i
n
t
o
f
A
B
)
∴
C
M
=
M
A
=
1
2
A
B
Suggest Corrections
1
Similar questions
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 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 AC at D. Show that
C
M
=
M
A
=
1
2
A
B
[4 MARKS]
Q.
Question 7 (iii)
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 AC at D. Show that
C
M
=
M
A
=
1
2
A
B
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.
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
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Criteria for Congruency
MATHEMATICS
Watch in App
Explore more
SAS Criteria for Congruency
Standard IX Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app