KnowledgeBoat Logo
|

Mathematics

In quadrilateral ABCD, diagonals AC and BD intersect at point E such that

AE : EC = BE : ED.

Show that : ABCD is a trapezium.

Similarity

7 Likes

Answer

Quadrilateral ABCD is shown in the figure below:

In quadrilateral ABCD, diagonals AC and BD intersect at point E such that AE : EC = BE : ED. Show that : ABCD is a trapezium. Similarity, Concise Mathematics Solutions ICSE Class 10.

Given,

AE : EC = BE : ED

⇒ AEEC=BEED\dfrac{AE}{EC} = \dfrac{BE}{ED}

⇒ AEBE=ECED\dfrac{AE}{BE} = \dfrac{EC}{ED}

⇒ ∠AEB = ∠DEC [Vertically opposite angles are equal]

∴ △AEB ~ △DEC [By SAS]

Since, △AEB ~ △DEC.

∴ ∠ECD = ∠EAB

Since, the above pair is a pair of alternate angles.

We can say that AB || DC.

Hence, proved that ABCD is a trapezium.

Answered By

2 Likes

Related Questions