Question

Use the figure below.


Select all the lines in the proof of △ABC≅△CDA that have the correct justification.

∠ACB≅∠CAD, Alternate Interior Angles Theorem

△ABC≅△CDA, SAS Triangle Congruence Theorem

∠BAC≅∠DCA, Alternate Interior Angles Theorem

AB || CD and BC || AD, ASA Triangle Congruence Theorem

AC≅AC, Reflexive Property of Congruence

Answer 1

Answer:

∠ACB≅∠CAD, Alternate Interior Angles Theorem

∠BAC≅∠DCA, Alternate Interior Angles Theorem

AC≅AC, Reflexive Property of Congruence

By A-S-A congruence, the △ABC≅△CDA.

Step-by-step explanation:

Given the figure:

We are given that:

Side BC || AD

Side AB || DC

Let us have a look at a few properties first.

Alternate Interior Angle Theorem: It states that when two parallel lines are cut by a line then the alternate angles which are on the interior side are equal to each other.

Reflexive Property of Congruence: It states that a side or angle is always congruent to itself.

Now, let us consider the triangles:

△ABC and △CDA.

Side BC || AD

Therefore,

∠ACB≅∠CAD, Alternate Interior Angles Theorem

Side AB || DC

Therefore,

∠BAC≅∠DCA, Alternate Interior Angles Theorem

Also, Side AC is common.

AC≅AC, Reflexive Property of Congruence

Therefore, by A-S-A congruence, the △ABC≅△CDA.