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Byju's Answer
Standard VII
Mathematics
Equal Angles Subtend Equal Sides
PQR is a tria...
Question
P
Q
R
is a triangle right angled at
P
and
M
is a point on
Q
R
such that
P
M
⊥
Q
R
show that
P
M
2
=
Q
M
.
M
R
.
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Solution
If a perpendicular is drawn from the vertex of the right angle to the
hypotenuse then
triangle on high side of the perpendicular are same.
So,
Δ
P
M
R
∼
Δ
Q
M
P
If two triangles are similar then the ratio is
P
M
Q
M
=
M
R
M
P
P
M
×
M
P
=
M
R
×
Q
M
P
M
=
M
R
×
Q
M
Suggest Corrections
3
Similar questions
Q.
P
Q
R
is a triangle right angled at
P
and
M
is a point on
Q
R
such that
P
M
⊥
Q
R
.
Show that
P
M
2
=
Q
M
.
M
R
Q.
PQR is a triangle right-angled at P and M is a point on QR such that
P
M
⊥
Q
R
. Show that
P
M
2
=
Q
M
×
M
R
[3 MARKS]
Q.
Question 2
PQR is a triangle right angled at P and M is a point on QR such that
P
M
⊥
Q
R
. Show that
P
M
2
=
Q
M
×
M
R
.
Q.
S
and
T
are points on sides
P
R
and
Q
R
of
△
P
Q
R
such that
∠
P
=
∠
R
T
S
. Show that
△
R
P
Q
∼
△
R
T
S
.
Q.
M and N are the mid-points of the sides QR and PQ respectively of a
Δ
PQR, right-angled at Q. Prove that
P
M
2
+
R
N
2
=
5
M
N
2
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Equal Angles Subtend Equal Sides
Standard VII Mathematics
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