Home
Class 10
MATHS
Any line parallel to the parallel sides ...

Any line parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally.

Text Solution

Verified by Experts

A trapezim ABCD in which AB||DC.
Also a line EF||AB||DC.
To prove , ` (AE)/(ED) = ( BG)/(GD)`
Also in ` DeltaBDC,` since GF||DC
`(BF)/(FC) = (BG)/(GD)` ( by B.P theorem)
From (1) and (2) ,we have
` (AE)/(ED) = (BF)/(FC)` Hecne proved
Promotional Banner

Topper's Solved these Questions

  • TRIANGLES

    NAGEEN PRAKASHAN|Exercise Problems From NCERT/ Exemplar|14 Videos

  • TRIANGLES

    NAGEEN PRAKASHAN|Exercise Exercise 6a|23 Videos

  • STATISTICS

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|5 Videos

  • VOLUME AND SURFACE AREA OF SOLIDS

    NAGEEN PRAKASHAN|Exercise Revisions Exercise Long Answer Questions|5 Videos

Similar Questions

Explore conceptually related problems

Consider the following statements : 1. The diagonals of a trapezium divide each other proportionally. 2. Any line drawn parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally. Which of the above statements is/are correct?

Prove that the segment joining the middle points of two non-parallel sides of a trapezium is parallel to the parallel sides and half of their sum.

If two non-parallel sides of a trapezium are equal; it is cyclic.

If two non-parallel sides of a trapezium are equal; it is cyclic.

Draw a trapezium and state the pair of parallel side

Examples: Prove that the segment joining the middle points of two non parallel sides od a trapezim is parallel to the parallel sides and half of their sum.

The parallel sides fo a trapezium are 30 cm and 20 cm and its non-parallel sides are both equal. If the area fo the trapezium is 300 cm^(2) , then what is the length (in cm) of eac non-parallel side?