99pts will give brainliest use the diagram and given information to answer the questions and prove the statement. given: x z prove: [see image] re-draw the diagram of the overlapping triangles so that the two triangles are separated.
what additional information would be necessary to prove that the two triangles, xby and zay, are congruent?
what congruency theorem would be applied?
prove using a list/flow chart proof.

The diagram shows angles x and z to be congruent.
it also shows segments xy and zy to be congruent.
there is enough info in the figure to prove the triangles congruent.

the given statement does not mean anything.
"given: x y" has no meaning. x and y with no other symbols are simply points x and y. what is the meaning of "given: x y"?

using the info in the figure, we can write this proof.

statements                                                                      reasons
1. < x is congruent to < z                              1. given in the figure
2. seg. xy is congr to seg zy            2. given in the figure
3. < y is congr to < y                                          3. congruence of angles is reflexive
4. tr xby is congr tr zay                          4. asa

we use the asa theorem of congruence of triangles.

answer:

step-by-step explanation:

from the given figure, consider xby and zay be two   different triangles having xy=zy and m∠x=m∠z.

thus, from δxby and δzay, we have

m∠x=m∠z(given)

xy=zy (given)

m∠y=m∠y(common)

therefore, by asa rule, δxby ≅ δzay.

thus, the additional information necessary to prove the two triangles congruent will be that m∠y=m∠y(common).