Question
- In each of the following, choose at least one word from parallelogram, rectangle,
rhombus, trapezoid, kite, or square, so that the resulting sentence is true. If none of
the words makes the sentence true, answer “none.”
a quadrilateral whose diagonals are equal and bisect each other.
b. a quadrilateral whose diagonals are perpendicular and bisects each
b. ather.
a quadrilateral whose diagonals are equal, perpendicular and they
d. other
rhombus, trapezoid, kite, or square, so that the resulting sentence is true. If none of
the words makes the sentence true, answer “none.”
a quadrilateral whose diagonals are equal and bisect each other.
b. a quadrilateral whose diagonals are perpendicular and bisects each
b. ather.
a quadrilateral whose diagonals are equal, perpendicular and they
d. other
Ask by Welch Rodriquez. in Ethiopia
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a. Rectangle or Square
b. Rhombus or Square
c. Square
b. Rhombus or Square
c. Square
Solution
Let’s analyze each statement one by one and determine which geometric shape fits the description.
a. A quadrilateral whose diagonals are equal and bisect each other.
- Parallelogram: Yes, the diagonals bisect each other, but they are not necessarily equal.
- Rectangle: Yes, the diagonals are equal and bisect each other.
- Rhombus: Yes, the diagonals bisect each other, but they are not equal.
- Trapezoid: No, this does not apply.
- Kite: No, this does not apply.
- Square: Yes, a square is a special case of a rectangle and a rhombus.
Answer: Rectangle (or Square)
b. A quadrilateral whose diagonals are perpendicular and bisect each other.
- Parallelogram: No, the diagonals do not have to be perpendicular.
- Rectangle: No, the diagonals are not perpendicular.
- Rhombus: Yes, the diagonals are perpendicular and bisect each other.
- Trapezoid: No, this does not apply.
- Kite: Yes, the diagonals are perpendicular, but they do not necessarily bisect each other.
- Square: Yes, a square is a special case of a rhombus.
Answer: Rhombus (or Square)
c. A quadrilateral whose diagonals are equal, perpendicular, and they bisect each other.
- Parallelogram: No, the diagonals are not necessarily equal.
- Rectangle: No, the diagonals are equal but not perpendicular.
- Rhombus: Yes, the diagonals are perpendicular and bisect each other, but they are not equal.
- Trapezoid: No, this does not apply.
- Kite: Yes, the diagonals are perpendicular, but they are not equal.
- Square: Yes, a square meets all these conditions.
Answer: Square
Summary of Answers:
- a. Rectangle (or Square)
- b. Rhombus (or Square)
- c. Square
If you have any further questions or need additional explanations, feel free to ask!
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution The Deep Dive
A quadrilateral whose diagonals are equal and bisect each other is a rectangle or a rhombus.
A quadrilateral whose diagonals are perpendicular and bisect each other is a rhombus or a square.
A quadrilateral whose diagonals are equal, perpendicular, and they bisect each other is a square.
