Question

2/2 rectangles, rhombus, squares practice day

1. if wxyz is a square with wz = 27, find each measure.

a) zy =

b) wy =

c) rx =

d) ( mangle wrz = )

e) ( mangle xyz = )

f) ( mangle zwy = )

27 54 13.5 90 45 180 38.2 42.8 19.1 22.6

Explanation:

Step1: Find side length ZY

All sides of a square are equal. Since $WZ=27$, $ZY=WZ=27$.

Step2: Find diagonal WY

Diagonal of square: $d = s\sqrt{2}$. Here $s=27$, so $WY=27\sqrt{2}\approx38.2$.

Step3: Find segment RX

Diagonals of square bisect each other. $RX=\frac{WY}{2}=\frac{27\sqrt{2}}{2}\approx19.1$.

Step4: Find $m\angle WRZ$

Diagonals of square are perpendicular, so $m\angle WRZ=90^\circ$.

Step5: Find $m\angle XYZ$

All angles of square are right angles, so $m\angle XYZ=90^\circ$.

Step6: Find $m\angle ZWY$

Diagonals of square bisect angles. Square angles are $90^\circ$, so $m\angle ZWY=\frac{90^\circ}{2}=45^\circ$.

Answer:

a) $ZY=27$
b) $WY\approx38.2$
c) $RX\approx19.1$
d) $m\angle WRZ=90$
e) $m\angle XYZ=90$
f) $m\angle ZWY=45$