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Standard IX
Mathematics
Question
In triangle ABC,
A
B
=
A
C
;
B
E
⊥
A
C
and
C
F
⊥
A
B
.
State whether following statement is true or false
A
F
=
A
E
True
False
A
True
B
False
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Solution
Verified by Toppr
In
△
B
F
C
and
△
B
E
C
,
B
C
=
B
C
(Common)
∠
F
C
B
=
∠
E
B
C
(Given, AB = AC)
∠
B
F
C
=
∠
B
E
C
(each
90
∘
)
Thus,
△
B
F
C
≅
△
C
E
B
(ASA rule)
Hence,
B
F
=
C
E
(By cpct)
A
B
=
A
C
(Given)
Hence,
A
B
−
B
F
=
A
C
−
C
E
A
F
=
A
E
Was this answer helpful?
1
Similar Questions
Q1
In triangle ABC,
A
B
=
A
C
;
B
E
⊥
A
C
and
C
F
⊥
A
B
.
State whether following statement is true or false
A
F
=
A
E
View Solution
Q2
In triangle ABC, AB = AC; BE
⊥
AC and CF
⊥
AB. Prove that :
(i) BE =CF
(ii) AF = AE
View Solution
Q3
In
△
A
B
C
,
A
B
=
A
C
;
B
E
⊥
A
C
and
C
F
⊥
A
B
. Prove that :
A
F
=
A
E
.
View Solution
Q4
State whther the following statement is true or false
In
△
A
B
C
,
A
B
=
A
C
;
B
E
⊥
A
C
and
C
F
⊥
A
B
. Then
B
E
=
C
F
View Solution
Q5
In triangle ABC;
A
B
=
A
C
,
B
D
⊥
A
C
and
C
F
⊥
A
B
.
then
B
A
=
C
F
.
If the above statement is true then mention answer as 1, else mention 0 if false
View Solution