CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Prove that any line parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally.


Open in App
Solution

Step 1: Note the given data

Let ABCD be a trapezium with ABDC

AD and BC are non-parallel sides.

Let, EF be a line parallel to AB,DC.

Join AC such that ACD and ACB are triangles and AC meets EF at G.

Step 2: Apply Thales theorem on ACD and ACB

Basic Proportionality Theorem: In a triangle, a line drawn parallel to one side to intersect the other sides distinct points divides two sides in same ratio.

In ACD

Here, EGDC. According to Basic Proportionality Theorem

AEED=AGGC……………..(i)

In ACB

Here, GFAB. According to Basic Proportionality Theorem

FCBF=GCAGBFFC=AGGC......................(ii)

Equating equation (i) and equation (ii)

AEED=BFFC

Hence proved that a line drawn parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally.


flag
Suggest Corrections
thumbs-up
16
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Equation of Line perpendicular to a given Line
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon