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In , points on and on are such that , , and…
MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles
Problem
In
△
X
Y
Z
\triangle XYZ
△
X
Y
Z
, points
P
P
P
on
X
Y
XY
X
Y
and
Q
Q
Q
on
X
Z
XZ
X
Z
are such that
X
P
=
3
cm
XP = 3\,\text{cm}
X
P
=
3
cm
,
P
Y
=
4.5
cm
PY = 4.5\,\text{cm}
P
Y
=
4.5
cm
,
X
Q
=
5
cm
XQ = 5\,\text{cm}
X
Q
=
5
cm
and
Q
Z
=
7.5
cm
QZ = 7.5\,\text{cm}
QZ
=
7.5
cm
. (a) Show that
P
Q
∥
Y
Z
PQ \parallel YZ
P
Q
∥
Y
Z
. (b) If
X
Y
XY
X
Y
is produced to a point
R
R
R
so that
Y
R
=
X
P
YR = XP
Y
R
=
X
P
, calculate
X
R
XR
X
R
.
Related theory
Ratios
Ratio and Proportion
Basic Proportionality Theorem
Similarity
Basic Proportionality Theorem (BPT)
Triangles
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