Final answer:
To prove XNW = ZXNY in a rhombus, we show that corresponding sides and angles of the two triangles are congruent.
Step-by-step explanation:
To prove XNW = ZXNY, we need to show that the corresponding sides and angles of the two triangles XNW and ZXNY are congruent.
- Given: Rhombus WXYZ
- From the properties of a rhombus, we know that all sides of a rhombus are congruent. Therefore, XY = XW = YZ.
- From the definition of a rhombus, we also know that the diagonals of a rhombus bisect each other at right angles. Therefore, XN is congruent to ZN and WN is congruent to YN.
- By the properties of congruent triangles, if the corresponding sides and angles of two triangles are congruent, the triangles are congruent. Therefore, XNW is congruent to ZXNY.
- And if two triangles are congruent, their corresponding parts are congruent. Therefore, XN = ZX, WN = ZY, and XW = YN.
Therefore, XNW = ZXNY.