Aline parallel to side BC of a triangle ABC, intersects AB and AC at D and E. prove that AD/DB=AE/EC.
Answers
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
Concept used:
Basic proportionality theorem(Thales theorem):
If a line is drawn parallel to one side of a triangle then it cuts other two sides proportionally.
In ΔABC, DE || BC
By Thales theorem,
Taking reciprocals
Adding 1 on both sides
Taking reciprocals once again, we get
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Amitnrw★ Brainly Teacher ★
Answer:
Proved
Step-by-step explanation:
If a line intersects sides AB and AC of a triangle ABC at D and E respectively and is parallel to BC, prove that AD/AB=AE/AC.
DE ║ BC
in ΔABC & ΔADE
∠A = ∠A Common Angle
∠ADE = ∠ABC as BC ║ DE
∠AED = ∠ACB as BC ║ DE
All three angles are equal
so
ΔABC ≅ ΔADE
in similar triangles
AD/AB =AE/AC = DE/BC
=> AD/AB =AE/AC
QED