Question

similar figures test (topic 5)
△pig is similar to △cat
which proportion is correct?
○ \\(\frac{pi}{ca}=\frac{ig}{at}\\)
○ \\(\frac{pi}{at}=\frac{pg}{ct}\\)
○ \\(\frac{pg}{ct}=\frac{pi}{ca}\\)
○ \\(\frac{pi}{ca}=\frac{pg}{ct}\\)

Explanation:

Step1: Recall similar - triangle property

For similar triangles $\triangle PIG$ and $\triangle CAT$, the ratios of corresponding sides are equal. That is, if $\triangle PIG\sim\triangle CAT$, then $\frac{PI}{CA}=\frac{IG}{AT}=\frac{PG}{CT}$.

Step2: Analyze options

Check each option to see if it represents the ratio of corresponding sides.

• Option 1: $\frac{PI}{AT}=\frac{PG}{CT}$ - Incorrect, as $PI$ and $AT$ are not corresponding sides.
• Option 2: $\frac{PI}{CT}=\frac{PG}{CA}$ - Incorrect, as the sides are not paired correctly.
• Option 3: $\frac{PI}{CA}=\frac{PG}{CT}$ - Correct, as $PI$ corresponds to $CA$ and $PG$ corresponds to $CT$.
• Option 4: $\frac{PI}{CA}=\frac{IG}{TC}$ - Incorrect, as $IG$ corresponds to $AT$ not $TC$.

Answer:

$\frac{PI}{CA}=\frac{PG}{CT}$ (corresponding to the correct - option in the multiple - choice format: the option that states $\frac{PI}{CA}=\frac{PG}{CT}$)