draw an angle XAY on your notebook and on ray AX, mark point B1,B2,B3,B4 and B such that AB1=B1B2=B2B3=B3B4=B4B . similarly on ray AY, mark point C1, C2, C3, C4 and C such that AC1= C1C2=C2C3= C3C4= C4C. then join B1C1 and BC
Answers
Answer:
similarly on ray AY, mark point C1, C2, C3, C4 and C such that AC1= C1C2=C2C3= C3C4= C4C. then join B1C1 and BC. 1. See answer.
Given : an angle XAY on your notebook and on ray AX, mark point B₁,B₂,B₃,B₄ and B such that AB₁=B₁B₂=B₂B₃=B₃B₄=B₄B .
similarly on ray AY, mark point C₁, C₂, C₃, C₄ and C such that AC₁= C₁C₂=C₂C₃= C₃C₄= C₄C
B₁C₁ and BC
To Find : Prove converse of Thales theorem:
Solution:
Thales theorem :
if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
Converse of Thales theorem
if a line intersects two sides of triangle in same ratio then line is parallel to third side
in ΔAB₁C₁ and ΔABC
AB₁/AB = AC₁ /AC as per construction
∠A = ∠A common
=> ΔAB₁C₁ ~ ΔABC
=> ∠AB₁C₁ = ∠ABC
As corresponding angles are equal
Hence B₁C₁ || BC
=> Converse of Thales theorem is Proved
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