Algebra Test If line yx is parallel to the side EF of trangle DEF, DE=10,DY=s, Do=ether and XF. D у Y x E
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Step-by-step explanation:
Given A△DEF and a point X inside it. Point X is joined to the vertices D, E and F. P is any point on DX. PQ||DE and QR||EF.
To prove PR||DF
Construction joins PR.
Proof In △XED, we have
PQ∣∣DE
∴
PD
XP
=
QE
XQ
(i)
In △XEF, we have
QR∣∣EF
∴
QE
XQ
=
RF
XR
(ii)
From (i) and (ii), we have
PD
XP
=
RF
XR
Thus, in △XFD, points R and P are dividing sides EF and XD in the same ratio. Therefore, by the converse of Basic Proportionality Theorem, we have
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