(i Can clean this up if needed, i just need a quick awnser)
Use Diagonals
1 of of 2 Questions
Question
Use the diagram and information to answer the question.

Given: V
is the midpoint of XZ¯¯¯¯¯¯¯¯.

∠1≅∠2

Prove: Quadrilateral WXYZ
is a parallelogram.

Quadrilateral W X Y Z with segments W Y and X Z that intersect at point V. Angles Y W Z and W Y X are congruent.

© 2019 StrongMind. Created using GeoGebra.


You can prove that KLMN
is a parallelogram by showing that its diagonals bisect each other.

Which plan should you use to prove that the diagonals bisect each other?

Responses

Use ∠1≅∠2,
∠3≅∠4,
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to show △WYZ≅△XZY
by the ASA Congruence Theorem. Then, use WV¯¯¯¯¯¯¯¯¯≅YV¯¯¯¯¯¯¯¯
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to prove WY¯¯¯¯¯¯¯¯¯
and XZ¯¯¯¯¯¯¯¯
bisect each other.
Use ∠1≅∠2,
∠3≅∠4,
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to show △WYZ≅△XZY
by the ASA Congruence Theorem. Then, use WV¯¯¯¯¯¯¯¯¯≅YV¯¯¯¯¯¯¯¯
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to prove line segment cap w cap y and line segment cap x cap z bisect each other.

Use ∠1≅∠2,
∠3≅∠4,
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to show △WVZ≅△YVX
by the AAS Congruence Theorem. Then, use WV¯¯¯¯¯¯¯¯¯≅YV¯¯¯¯¯¯¯¯
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to prove WY¯¯¯¯¯¯¯¯¯
and XZ¯¯¯¯¯¯¯¯
bisect each other.
Use ∠1≅∠2,
∠3≅∠4,
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to show △WVZ≅△YVX
by the AAS Congruence Theorem. Then, use WV¯¯¯¯¯¯¯¯¯≅YV¯¯¯¯¯¯¯¯
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to prove line segment cap w cap y and line segment cap x cap z bisect each other.

Use ∠1≅∠2,
∠3≅∠4,
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to show △WVZ≅△XVY
by the ASA Congruence Theorem. Then, use WV¯¯¯¯¯¯¯¯¯≅YV¯¯¯¯¯¯¯¯
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to prove WY¯¯¯¯¯¯¯¯¯
and XZ¯¯¯¯¯¯¯¯
bisect each other.
Use ∠1≅∠2,
∠3≅∠4,
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to show △WVZ≅△XVY
by the ASA Congruence Theorem. Then, use WV¯¯¯¯¯¯¯¯¯≅YV¯¯¯¯¯¯¯¯
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to prove line segment cap w cap y and line segment cap x cap z bisect each other.

Use ∠1≅∠2,
∠3≅∠4,
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to show △WYZ≅△XZY
by the AAS Congruence Theorem. Then, use WV¯¯¯¯¯¯¯¯¯≅YV¯¯¯¯¯¯¯¯
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to prove WY¯¯¯¯¯¯¯¯¯
and XZ¯¯¯¯¯¯¯¯
bisect each other.
Use ∠1≅∠2,
∠3≅∠4,
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to show △WYZ≅△XZY
by the AAS Congruence Theorem. Then, use WV¯¯¯¯¯¯¯¯¯≅YV¯¯¯¯¯¯¯¯
and XV¯¯¯¯¯¯¯¯≅ZV¯¯¯¯¯¯¯¯
to prove line segment cap w cap y and line segment cap x cap z bisect each other.