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Standard VIII
Mathematics
Congruency of Triangles
43. In triang...
Question
43. In triangle ABC, angle BAC=90 degree and AB=BC.seg AP is perpendicular on side BC. B-P-C.D is any point on side BC. prove that 2AD2=BD2+CD2
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Similar questions
Q.
In
U
A
B
C
^
e
B
A
C
=
90
o
,
A
B
=
A
C
s
e
g
A
P
o
side
B
C
,
B
−
P
−
C
.
D
is any points on side
B
C
. Prove that:
2
A
D
2
=
B
D
2
+
C
D
2
Q.
In an isosceles triangle
A
B
C
with
A
B
=
A
C
,
B
D
is perpendicular from
B
to side
A
C
.
Prove that
B
D
2
−
C
D
2
=
2
C
D
.
A
D
Q.
In an isosceles triangle ABC with AB = AC, BD is perpendicular from B to the side AC. Prove that
B
D
2
−
C
D
2
=
2
C
D
.
A
D
Q.
In this question
In a triangle ABC , AB>AC , AD is perpendicular to BC , prove that
AB 2 - AC
2
= BD 2= CD2
I have done it like this
In triangle ABD
AD2. = AB2 -. BD2. EQUATION 1
In triangle ADC
AD2 =. AC2 - CD2. EQUATION 2
on combining. EQUATION 1 and 2
AD2 = AB2. -. BD 2
AD2 = AC2 - CD2.
AB2 -. AC2 =. BD2 - CD2
hence proved
IS THIS CORRECT
Q.
In triangle
A
B
C
,
A
D
is perpendicular to
B
C
.Prove that:
A
B
2
−
A
C
2
=
B
D
2
−
C
D
2
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