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

State and prove Basic Proportionality theorem.

Open in App
Solution

Basic Proportionality Theorem states that, if a line is parallel to a side of a triangle which intersects the other sides into two distinct points,then the line divides those sides of the triangle in proportion.

Let ABC be the triangle.

The line l parallel to BC intersect AB at D and AC at E.

To prove ADDB=AEEC

Join BE,CD

Draw EFAB, DGCA

Since EFAB,

EF is the height of triangles ADE and DBE

Area of ADE=12× base × height=12AD×EF

Area of DBE=12×DB×EF
areaofΔADEareaofΔDBE=12×AD×EF12×DB×EF=ADDB ........(1)
Similarly,
areaofΔADEareaofΔDCE=12×AE×DG12×EC×DG=AEEC ......(2)

But ΔDBE and ΔDCE are the same base DE and between the same parallel straight line BC and DE.

Area of ΔDBE= area of ΔDCE ....(3)

From (1), (2) and (3), we have

ADDB=AEEC
Hence proved.

631188_605043_ans_86bdeb7b2b9e44bebdbad9319f8f5241.png

flag
Suggest Corrections
thumbs-up
8
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Basic Proportionality Theorem
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon