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`