A line is drawn through the vertex A parallel to the base of the triangle ABC, write the length of PQ distance between parallel lines in this way, how many triangle of same area can be drawn?
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R.E.F image
Given, AB=3AP...(1)
we can prove the two triangles
are similar using
1) AA (Angle-Angle)
2) SSS (side-side-side)
3) SAS (side-Angle-side)
In this case.
∠A is common to both the
ΔABC and ΔAPQ
Also, ∠B≅∠P (corresponding angles)
∴ using AA theorem it is proved
that ΔABC∼ΔAPQ
[Note :- Similarity sign is ∼]
Therm : The two similar Δs , the ratio of
their area is the square of the
ratio of their sides.
Hence.
AreaofΔAPQ
AreaofΔABC
=
(AP)
2
(AB)
2
=(
AP
AB
)
2
from (1)
AreaofΔABC
AreaofΔAPQ
=(
AB
AP
)
2
=(
3
1
)
2
=
9
1
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