In the given figure, AD = 2cm, BD = 3 cm, AE = 3.5 cm and AC = 7 cm. Is DE parallel to BC ?
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10th
Maths
Triangles
Basic Proportionality Theorem (Thales Theorem)
In the adjoining figure, DE...
MATHS
In the adjoining figure, DE || AB, AD = 7 cm, CD = 5 cm and BC = 18 cm. Find BE and CE.
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ANSWER
The basic proportionality theorem states that if a line is drawn parallel to one side of a triangle and it intersects the other two sides at two distinct points then it divides the two sides in the same ratio.
It is given that DE∣∣AB,AD=7 cm, CD=5 cm and BC=18 cm.
Using the basic proportionality theorem, we have
CA
CD
=
AB
DE
=
CB
CE
⇒
CA
CD
=
CB
CE
⇒
12
5
=
18
CE
⇒18×5=12CE
⇒12CE=90
⇒CE=
12
90
=7.5
Since CE=7.5 cm, therefore,
CB=CE+EB
⇒18=7.5+EB
⇒EB=18−7.5=10.5
Hence, BE=10.5 cm and CE=7.5 cm.
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