Question

Complete the proof.FGiven: BAI ACDC I ACProve: ABFAACFDStatementsReasons1. Given1. Given: BAI ACDC I AC2. BA|| DC2. If two lines are perpendicular to a third line,then the two lines are parallel.3.II4. AZAD43. If two parallel lines are cut by a transversal,I alternate interior angles are congruent.I4.14. ABFAACFD:: ZDFC = ZBFA; ZDAB ZBCD:: ZCBA - ZADC; ZBAD ~ ZDCB:: Angle-Angle (AA) postulate:: Side-Angle-Side (SAS) postulate):: ZCDA ZBAD; ZCBA ZBCD

Answer 1

It is given that

BA is perpendicular to AC and

CD is perpendicular to AC

We need to prove that

`\Delta ABF\approx\Delta CFD`

Now

`\angle BFA=\angle CFD\text{ (vertically opposite angles ) }`

And since lines AB and CD are parallel so

`\angle\text{ABF}=\angle DCF\text{ (Alternate angles ) }`

So by AA criteria

`\Delta ABF\approx\Delta CFD`