Question

△efg ~ △xyz. complete each statement.
a. ∠f ≅?
b. ∠z ≅?
c. $\frac{fg}{yz}=\frac{?}{xz}$
d. $\frac{ef}{xy}=\frac{fg}{?}$

Explanation:

Step1: Recall property of similar triangles

For similar triangles $\triangle EFG\sim\triangle XYZ$, corresponding angles are congruent and corresponding - sides are in proportion.

Step2: Find congruent angles for part a

The corresponding angle to $\angle F$ in $\triangle XYZ$ is $\angle Y$. So, $\angle F\cong\angle Y$.

Step3: Find congruent angles for part b

The corresponding angle to $\angle Z$ in $\triangle EFG$ is $\angle G$. So, $\angle Z\cong\angle G$.

Step4: Find the ratio of sides for part c

Since the sides of similar triangles are in proportion, if $\frac{FG}{YZ}=\frac{?}{XZ}$, the missing side in the ratio is $EG$. So, $\frac{FG}{YZ}=\frac{EG}{XZ}$.

Step5: Find the ratio of sides for part d

If $\frac{EF}{XY}=\frac{FG}{?}$, the missing side in the ratio is $YZ$. So, $\frac{EF}{XY}=\frac{FG}{YZ}$.

Answer:

a. $\angle Y$
b. $\angle G$
c. $EG$
d. $YZ$