Question

△acb ~ △qrs. complete each statement. a. ∠a ≅ ? b. ∠r ≅ ? c. $\frac{ab}{qs}=\frac{?}{qr}$ d. $\frac{bc}{sr}=\frac{ca}{?}$

Explanation:

Step1: Recall similar - triangle properties

When $\triangle ACB\sim\triangle QRS$, corresponding angles are congruent and corresponding sides are in proportion.

Step2: Find congruent angles for part a

The corresponding angle to $\angle A$ in $\triangle QRS$ is $\angle Q$. So, $\angle A\cong\angle Q$.

Step3: Find congruent angles for part b

The corresponding angle to $\angle R$ in $\triangle ACB$ is $\angle B$. So, $\angle R\cong\angle B$.

Step4: Find the proportion of sides for part c

Since the sides are in proportion, if $\frac{AB}{QS}=\frac{?}{QR}$, the corresponding side to $AB$ with respect to $QR$ is $AC$. So, $\frac{AB}{QS}=\frac{AC}{QR}$.

Step5: Find the proportion of sides for part d

If $\frac{BC}{SR}=\frac{CA}{?}$, the corresponding side to $CA$ with respect to $SR$ is $RQ$. So, $\frac{BC}{SR}=\frac{CA}{RQ}$.

Answer:

a. $\angle Q$
b. $\angle B$
c. $AC$
d. $RQ$