Question

triangle $\triangle abc$ is the result of dilating $\triangle abc$ about point $p$ by a scale factor of $\dfrac{5}{2}$.

determine whether each claim about the properties of $\triangle abc$ and $\triangle abc$ is true or false.

the measures of $\angle c$ and $\angle c$ are equal. \quad true/false

the areas of $\triangle abc$ and $\triangle abc$ are the same. \quad true/false

Explanation:

Step1: Analyze angle measure in dilation

Dilation is a similarity transformation. Similar figures have corresponding angles equal. So, $\angle C$ and $\angle C'$ (corresponding angles) should be equal.

Step2: Analyze area in dilation

The scale factor of dilation is $\frac{5}{2}$. The ratio of areas of similar figures is the square of the scale factor. So, area of $\triangle A'B'C'$ is $(\frac{5}{2})^2=\frac{25}{4}$ times the area of $\triangle ABC$. Thus, areas are not the same.

Answer:

The measures of $\angle C$ and $\angle C'$ are equal: True
The areas of $\triangle ABC$ and $\triangle A'B'C'$ are the same: False