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Theorem 3 : Any line parallel to the sides of a trapezium (trapezoid) divides the non-parallel sides proportionally.

Given : ABCD is a trapezoid. DC AB. EF AB and EF DC.

Prove that : AE/ED = BF/FC

Construction : Join AC, meeting EF in G.

StatementsReasons1) EG DC1) Given (in Î”ADC)2) AE/ED = AG/GC2) By Basic proportionality theorem3) GF AB3) Given (in Î”ABC)4) AG/GC = BF/FC4)By Basic proportionality theorem5) AE/ED = BF/FC5) From (2) and (4)

Source: ask-math.com

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To prove that the line which divides the nonparallel sides of a trapezium proportionally is parallel to the third side, we can use the property of similar triangles. Let the trapezium ABCD have sides AB and CD as the nonparallel sides, and side BC as the third side. Let the line dividing AB and CD be denoted as EF, with E on AB and F on CD. By the property of similar triangles, we can show that triangles AEF and BCF are similar, and hence their corresponding angles are congruent. This proves that EF is parallel to BC.

Q: Prove that the line which divides the nonparallel sides of a trapezium proportionally is parallel to the third side.?

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The Equator divides the Earth into the Northern Hemisphere and the Southern Hemisphere. Lines of latitude are parallel to the Equator both to the north and to the south.

One pair of parallel sides, It divides in to smaller shapes

The equator or any of the lines of longitude (which meet at the poles).

A line drawn anywhere around earth creates a hemisphere. There are 4 hemispheres.

1 divides into 121 and 42.

Related questions

Similar shapes.

If a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally

Converse of the triangle proportionality theorem APEX :)

The Parallel line that divides the Earth in two is the Equator.Answer by Andres914

The parallel is called the equator.

The Equator is the parallel that divides the Earth into two equal halves - the Northern Hemisphere and the Southern Hemisphere. It is located at 0 degrees latitude.

The Equator divides the Earth into the Northern Hemisphere and the Southern Hemisphere. Lines of latitude are parallel to the Equator both to the north and to the south.

49th

The equator.

The equator.

equater

Equator