Question
Which of the following statements is true about a rectangle? I. Opposite sides are congruent. II. Opposite sides are parallel. il. Diagonals are congruent. N. Diagonals bisect the opposite angles. I and II only I, II, III, IV I, II, and III only I only
Ask by Lane Higgins. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The true statements about a rectangle are I, II, and III only.
Solution
A rectangle has the following properties:
• Opposite sides are congruent.
• Opposite sides are parallel.
• Diagonals are congruent.
However, the diagonals of a rectangle do not necessarily bisect the interior angles (this is true for a square, which is a special type of rectangle).
Therefore, the true statements about a rectangle are I, II, and III only.
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Simplify this solution Mind Expander
Rectangles are fascinating shapes, and the truths about them are even more interesting! Statement I is true because in a rectangle, the pairs of opposite sides are indeed congruent, meaning they have the same length. Plus, Statement II is spot on too—opposite sides are parallel, making rectangles a great example of quadrilaterals with such characteristics. Now for the diagonals! You’ll be thrilled to know that in a rectangle, the diagonals are indeed congruent, making Statement III true as well. However, Statement IV is a tad mischievous; while the diagonals bisect each other, they do not bisect the opposite angles. So, the correct answer would be I, II, and III only!
