Question

Fill in the missing blanks in the proof:

Given: Rhombus
WXYZ
Prove: XNW = ZXNY
W
X
Z
Statements
Y
1.
Rhombus
WXYZ
2. XY WZ = XW = YZ
3. XN ZN and WN YN
4. #C
5. ZXNW ZXNY
A choose your answer...
B choose your answer...
C choose your answer...
D choose your answer...
<
>
>
Reasons
1. Given
2. #A
3. #B
4. SSS
5. #

Answer 1

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.

1. Given: Rhombus WXYZ
2. From the properties of a rhombus, we know that all sides of a rhombus are congruent. Therefore, XY = XW = YZ.
3. 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.
4. 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.
5. And if two triangles are congruent, their corresponding parts are congruent. Therefore, XN = ZX, WN = ZY, and XW = YN.

Therefore, XNW = ZXNY.