Question
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IDS TURN WHATEVER AGE TH... A. All sides are the same length. B. Each interior angle measures \( 90^{\circ} \). C. Two of the interior angles each measure less thation \( 90^{\circ} \). D. Two sides have the same length. E. The measures of the interior angles have a sum of \( 90^{\circ} \).

Ask by Huang Bowers. in South Africa
Feb 17,2025

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Answer

A, B, and D are true for a square.

Solution

It looks like the problem is asking which of the following statements are true for a square. A square is defined as a quadrilateral with the following properties:  • All four sides are congruent.  • Each of its four interior angles measures 90°. Let’s look at the choices: A. All sides are the same length.  • This is true for a square. B. Each interior angle measures 90°.  • This is also true for a square. C. Two of the interior angles each measure less than 90°.  • In a square every interior angle is exactly 90°, so this is false. D. Two sides have the same length.  • Although this is a much weaker statement than “all sides are the same length,” it is still true; any two sides you pick in a square will indeed be equal. E. The measures of the interior angles have a sum of 90°.  • For any quadrilateral, including a square, the interior angles add up to 360° (not 90°), so this statement is false. Thus, the statements that hold true for a square are A, B, and D.

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Extra Insights

When we consider polygons and particularly triangles, it's important to pay attention to the relationships between sides and angles. For example, option B reflects the property of rectangles or squares, where all angles are right angles. This geometrical principle is vital in architecture and design, ensuring structural integrity and aesthetic appeal! Now, if you’re ever designing a room or constructing anything where right angles are needed, a handy tip is to always use the Pythagorean theorem! This classic relationship, \(a^2 + b^2 = c^2\), can help you ensure those corners are square, preventing any unfortunate tilting or misalignment as you build!

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