ABDC is a parallelogram in which diagonals AD and BC intersect at O. AE and DF are perpendicular on BC at E and F, respectively. Which of the following is not true?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. ∆ ADC ≅ ∆ ABD
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Understanding |
Application |
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In ∆ABC and ∆DBC: AC = BD, AB = DC and BC is the common side hence, triangles are congruent.
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In ∆ AEO and ∆ DOF: ∠AOE = ∠DOF (vertically opposite angle) ∠AEO = ∠DFO (both 90°) And AO = OD (BC bisects AD) Hence, the triangles are congruent
In ∆ AEB and ∆ DFC: ∠DFC = ∠AEB ∠ABE = ∠DCF CD = AB Hence, the triangles are congruent In ∆ ADC and ∆ ABD AC = BD AD = AD And CD = BA Hence ∆ ADC is congruent to ∆ DAB. But not congruent to ∆ ABD Hence statement 1 is not true. |
