Question

given Given AB‾∥DC‾AB ∥ DC and BC‾∥AD‾BC ∥ AD , prove △ABC≅△CDA△ABC≅△CDA by filling out the flowchart below.

Answer 1

Given:

$AB||DC,BC\mleft\Vert AD\mright?$

To show that,

$\Delta ABC\cong\Delta CDA$

First box:

$AB||DC(\text{Given)}$

Below box to the first box:

$\angle BAC=\angle DCA(Parallel\text{ lines cut by the transversal form congruent alternate interior angles)}$

Second box:

$BC\Vert AD(\text{Given)}$

Below box to the second box:

$\angle DAC=\angle BCA(Parallel\text{ lines cut by the transversal form congruent alternate interior angles}$

Third box in the second row:

$AC=AC\text{ (common side)}$

Last box:

So, using ASA congruence axiom,

$\Delta ABC\cong\Delta CDA$