Question

Given quadrilateral ABCD, where AB || CD, _ABC _ _CDA, and a diagonal AC. Which method can be used to prove TriangleABC _ TriangleCDA?

f Angle-Angle-Side (AAS)
g Side-Side-Angle (SSA)
h Side-Angle-Side (SAS)
j Side-Side-Side (SSS)

Answer 1

both triangles have the same angle and the two sides are parallel, ad and bc have to be congruent.
Then, because AC is shared by both triangles, we know it's the same for both, we now have two pairs congruent side and 1 congruent set of angles.

So side angle side.

Answer 2

Option f Angle Angle Side (AAS)

Explanation:

Given is a quadrilateral ABCD with two parallel sides AB and CD

AC the diagonal will also be a transveral and hence makes equal angles

(interior angles theorem)

Angle BAC = CAD

Also given that Angle ABC = angle CDA

AC =AC (reflexive property)

Hence by angle angle side axiom, the two triangles would be congruent

Option f( Angle Angle Side (AAS)