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)

Option f Angle Angle Side (AAS)

Step-by-step 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)

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

89

step-by-step explanation: