1. prove that if draw a line which is parllel to any side of a triangle and intersect the other tho side at differnt point. then this line divides these two line in the same ratio?
Answers
Given: In a △PQR, line l∥ side QR, line l intersect the sides PQ and PR in two distinct points M and N respectively.
To prove: MQPM=NRPN ... (i)
Construction: segQN and segRM are drawn.
Proof: A(△QMN)A(△PMN)=MQPM
(Both triangles have equal height with common vertex M)
∴A(△RMN)A(△PMN)=NRPN ... (ii)
But A(△QMN)=A(△RMN), because they are between parallel lines MN and QR and have equal height corresponding to their common base MN ..... (iii)
From (i), (ii) and (iii), we get
A(△QMN)A(△PMN)=A(△RMN)A(△PMN)
∴MQPM=NRPN [henceproved]
Answer:
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points prove that the other two sides are divided in the same ratio
Theorem: If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points , then the other two sides are divided in the same ratio.