wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Prove that, if a line parallel to a side of a triangle intersect the other sides in two distinct points, then the line divides those sides in proportion.

Open in App
Solution

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: PMMQ=PNNR ... (i)

Construction: segQN and segRM are drawn.

Proof: A(PMN)A(QMN)=PMMQ
(Both triangles have equal height with common vertex M)

A(PMN)A(RMN)=PNNR ... (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(PMN)A(QMN)=A(PMN)A(RMN)

PMMQ=PNNR [henceproved]

635320_599392_ans.png

flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Basic Proportionality Theorem
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon