Questions: Complete this sentence: After a congruence transformation, the area of a triangle would be it was before. A. less than B. the same as C. greater than D. cannot be determined

Complete this sentence: After a congruence transformation, the area of a triangle would be it was before. A. less than B. the same as C. greater than D. cannot be determined
Transcript text: Complete this sentence: After a congruence transformation, the area of a triangle would be $\qquad$ it was before. A. less than B. the same as C. greater than D. cannot be determined
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Solution

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Solution Steps

To determine the effect of a congruence transformation on the area of a triangle, we need to understand that congruence transformations include translations, rotations, and reflections, which do not alter the size or shape of a figure. Therefore, the area of the triangle remains unchanged.

Step 1: Understanding Congruence Transformations

A congruence transformation includes operations such as translations, rotations, and reflections. These transformations preserve the shape and size of geometric figures.

Step 2: Analyzing the Area of a Triangle

The area \( A \) of a triangle is determined by its base \( b \) and height \( h \) using the formula: \[ A = \frac{1}{2} b h \] Since congruence transformations do not change the dimensions of the triangle, both \( b \) and \( h \) remain constant.

Step 3: Conclusion on Area Change

As a result, the area of the triangle after a congruence transformation is the same as it was before the transformation. Therefore, we conclude that the area remains unchanged.

Final Answer

\(\boxed{B. \text{the same as}}\)

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