ABC is a trangle D is a point on AB such that AD =1/4 AB and E is a point on AC such that AE=1/4 AC . Prove that DE = 1/4 BC
Answers
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Answer:
AB
AD
=
4
1
and
AC
AE
=
4
1
[Given]
∴
AB
AD
=
AC
AE
⇒DE∥BC [By converse of basic proportionality theorem]
In △ADE and △ABC,
∠ADE=∠B [Pair of corresponding angles]
∠AED=∠C [Pair of corresponding angles]
Hence, △ADE∼△ABC [By AA similarity criteria]
Therefore,
AB
AD
=
AC
AE
=
BC
DE
[Corresponding sides of similar triangles are proportional]
∴
BC
DE
=
4
1
⇒BC=4DE
⇒BC=4×2
⇒BC=8cm
Step-by-step explanation: