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Join BD with a broken line to indicate an imaginary figure ABDE. AD as diagonal, we need both the given statements to prove that t'gle ABD and t'gle ADE are both congruent. Hence, Angles B and E are equal and opposite, so are angles A and D, and sides AB = BD = DE = AE.
Hence, ABDE will be a rhombus, if the given stimulus and statements are true. _________________
What's the OA for this one please? Is there anyone else that might want to give it a shot? I got (C) but really more because of intuition than because I can explain it clearly.
Experts please advice on this very nice piece of question Many thanks Will provide some Kudos to good answers Cheers J:)
Quadrilateral ABCD is a rhombus and points C, D, and E are on the same line. Is quadrilateral ABDE a rhombus?
Rhombus is a quadrilateral with all four sides equal in length. A rhombus is actually just a special type of parallelogram (just like square or rectangle).
So ABCD is a rhombus means AB=BC=CD=AD. ABDE to be a rhombus it must be true that AB=BD=DE=AE.
(1) The measure of angle BCD is 60 degrees --> diagonal BD equals to the sides of rhombus, so BD=AB. Know nothing about DE or/and AE. Not sufficient.
(2) AE is parallel to BD --> ABDE is a parallelogram (as AE||BD and BA||DE), hence opposite sides are equal: BD=AE and AB=DE. But we don't know whether all sides are equal (AB=BD=DE=AE). Not sufficient.
(1)+(2) From (1): BD=AB and from (2) BD=AE and AB=DE --> AB=BD=DE=AE --> ABDE is a rhombus. Sufficient.