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Standard IX
Mathematics
Question
Given altitudes in ABC. What additional information is needed to prove
△
A
F
D
≅
△
B
F
E
?
A
C
≅
B
C
A
E
≅
B
D
A
B
≅
B
C
D
F
≅
B
C
A
A
C
≅
B
C
B
A
B
≅
B
C
C
D
F
≅
B
C
D
A
E
≅
B
D
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Solution
Verified by Toppr
In
△
A
F
D
and
△
B
F
E
∠
A
F
D
≅
∠
B
F
E
..... (Opposite angles formed by lines
A
E
,
D
B
)
If it's given that
A
E
≅
B
D
Then,
A
F
≅
F
B
and
F
D
≅
E
F
Then by
S
A
S
postulate
△
A
F
D
and
△
B
F
E
are congruent.
Hence,
A
E
≅
B
D
is needed to prove the congruency of triangles.
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Similar Questions
Q1
Given altitudes in ABC. What additional information is needed to prove
△
A
F
D
≅
△
B
F
E
?
View Solution
Q2
If ABC is an isosceles triangle in which AC = BC, AD and BE are respectively two altitudes to sides BC and AC, then prove that AE = BD.
View Solution
Q3
A
B
C
is an isosceles triangle in which
A
C
=
B
C
A
D
and
B
E
are respectively two altitudes of side
B
C
and
A
C
. Prove that
A
E
=
B
D
.
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Q4
Question 9
If ABC is an isosceles triangle in which AC = BC, AD and BE are respectively two altitudes to sides BC and AC, then prove that AE = BD.
View Solution
Q5
In the isosceles
△
A
B
C
,
A
B
=
A
C
,
B
C
=
18
c
m
,
A
D
⊥
B
C
,
A
D
=
12
c
m
,
B
C
is produced to '
E
' and
A
E
=
20
c
m
. Prove that
∠
B
A
E
=
90
o
.
View Solution