Question
A student claims that all squares are congruent to each other. How do you respond? Choose the correct answer below. A. The student is incorrect. Although all squares have four congruent \( 90^{\circ} \) angles, any congruent squares must also have the same side lengths, which is not true for all squares. B. The student is correct. All squares have four \( 90^{\circ} \) angles, so their angles are congruent, meaning that all squares must be congruent C. The student is incorrect because not all squares have congruent angles. D. The student is correct. A square has four sides of the same length and four angles of the same measure, so all squares are congruent
Ask by Wang Montgomery. in the United States
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The student is incorrect. While all squares have four congruent \(90^\circ\) angles, congruent squares must also have the same side lengths, which is not true for all squares.
Solution
1. A square is defined as having four \(90^\circ\) angles and four sides of equal length.
2. While every square has four congruent angles, congruency between squares also requires having the same side lengths.
3. Since squares can have different side lengths, not all squares are congruent.
Thus, the correct answer is:
\( \textbf{A. The student is incorrect. Although all squares have four congruent } 90^\circ \textbf{ angles, any congruent squares must also have the same side lengths, which is not true for all squares.} \)
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Extra Insights
A. The student is incorrect. Although all squares have four congruent \(90^{\circ}\) angles, any congruent squares must also have the same side lengths, which is not true for all squares. D. The student is correct. A square has four sides of the same length and four angles of the same measure, so all squares are congruent.
