Question

1. in the figure shown below, $\triangle ade \sim \triangle abc$. complete the following statements.

a. if $\frac{ab}{ad}=5$, then $\frac{ac}{ae}=$
b. if $\frac{ac}{ae}=12$, then $\frac{bc}{\\;\\;\\;\\;}=12$
c. $m\angle aed = m\angle$

1. in the figure shown, $\triangle abc \sim \triangle dec$. complete the following statements.

a. if $\frac{ab}{de}=4$ then $\frac{ac}{dc}=$
b. if $\frac{ac}{de}=8$ then $\frac{bc}{\\;\\;\\;\\;}=8$
c. $m\angle abc = m\angle$

Explanation:

Step1: Use similar triangle side ratio

For similar triangles $\triangle ADE \sim \triangle ABC$, corresponding sides are proportional: $\frac{AB}{AD}=\frac{AC}{AE}$.
Given $\frac{AB}{AD}=5$, so $\frac{AC}{AE}=5$.

Step2: Match corresponding sides

For $\triangle ADE \sim \triangle ABC$, $\frac{AC}{AE}=\frac{BC}{DE}$.
Given $\frac{AC}{AE}=12$, so the missing side is $DE$.

Step3: Match corresponding angles

For $\triangle ADE \sim \triangle ABC$, $\angle AED$ corresponds to $\angle ACB$, so $m\angle AED = m\angle ACB$.

Step4: Use similar triangle side ratio

For similar triangles $\triangle ABC \sim \triangle DEC$, corresponding sides are proportional: $\frac{AB}{DE}=\frac{AC}{DC}$.
Given $\frac{AB}{DE}=4$, so $\frac{AC}{DC}=4$.

Step5: Match corresponding sides

For $\triangle ABC \sim \triangle DEC$, $\frac{AC}{DC}=\frac{BC}{EC}$.
Given $\frac{AC}{DC}=8$, so the missing side is $EC$.

Step6: Match corresponding angles

For $\triangle ABC \sim \triangle DEC$, $\angle ABC$ corresponds to $\angle DEC$, so $m\angle ABC = m\angle DEC$.

Answer:

Problem 8:

a. $5$
b. $DE$
c. $ACB$

Problem 9:

a. $4$
b. $EC$
c. $DEC$