Question

wednesday

1. each pair of polygons is similar. what do you know about the corresponding angles and sides? write 6 congruence statements:
2. simplify: $\frac{-15}{5}=$

is this number an integer, rational, or both?

1. solve each proportion:

$\frac{4}{11}=\frac{19}{x}$ $\frac{x}{21}=\frac{11}{30}$

Explanation:

Step1: Similar polygons properties

$\angle M=\angle Y$, $\angle P=\angle X$, $\angle O=\angle W$, $\angle N=\angle Z$, $\frac{MP}{XY}=\frac{PO}{XW}=\frac{ON}{WZ}=\frac{NM}{ZY}$

Step2: Simplify fraction

$\frac{-15}{5}=-3$

Step3: Determine number type

-3 is an integer and a rational number.

Step4: Solve proportion $\frac{4}{11}=\frac{19}{x}$

$4x = 19\times11$, $x=\frac{209}{4}=52.25$

Step5: Solve proportion $\frac{x}{21}=\frac{11}{30}$

$30x=21\times11$, $x=\frac{231}{30}=7.7$

Answer:

1. Angle - congruence and side - ratio statements as above.
2. -3; both
3. $x = 52.25$; $x = 7.7$