Questions: Triangle A'B'C' is the result of dilating ABC about point A by a scale factor of 2/3. Determine whether each claim about the properties of ABC and A'B'C' is true or false. The measures of angle B and angle B' are equal. True/false The coordinates of A and A' are the same. True/false

Triangle A'B'C' is the result of dilating ABC about point A by a scale factor of 2/3.

Determine whether each claim about the properties of ABC and A'B'C' is true or false.

The measures of angle B and angle B' are equal.
True/false

The coordinates of A and A' are the same.
True/false

Transcript text: Triangle $\triangle A^{\prime} B^{\prime} C^{\prime}$ is the result of dilating $\triangle A B C$ about point $A$ by a scale factor of $\frac{2}{3}$. Determine whether each claim about the properties of $\triangle A B C$ and $\triangle A^{\prime} B^{\prime} C^{\prime}$ is true or false. The measures of $\angle B$ and $\angle B^{\prime}$ are equal. True/false The coordinates of $A$ and $A^{\prime}$ are the same. True/false

Solution

Solution Steps

Step 1: Understanding the Dilation

The problem states that triangle $ \triangle A'B'C' $ is the result of dilating $ \triangle ABC $ about point $ A $ by a scale factor of $ \frac{2}{3} $.

Step 2: Analyzing the Angles

When a triangle is dilated, the angles remain the same. Therefore, the measures of $ \angle B $ and $ \angle B' $ are equal.

Step 3: Analyzing the Coordinates of Point A

Since the dilation is about point $ A $, the coordinates of $ A $ and $ A' $ are the same.