Question
Which of the following statements is true about a rhombus? I. Diagonals are congruent. II. Each diagonal of a rhombus bisects a pair of opposite angles. III. Rhombi are squares. N. All sides are congruent IN only I and IV only II and IV only i, II, ill, iv
Ask by Turner Bond. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Statements II and IV are true.
Solution
Let's examine each statement about a rhombus:
I. Diagonals are congruent.
• In a general rhombus, the diagonals are not congruent (only in a square, which is a special type of rhombus, are they congruent). So, this statement is false.
II. Each diagonal of a rhombus bisects a pair of opposite angles.
• This is true. Each diagonal of a rhombus bisects the angles at the vertices it connects.
III. Rhombi are squares.
• Not all rhombi are squares. A square is a special type of rhombus with all right angles. Thus, this statement is false.
IV. All sides are congruent.
• This is true by definition of a rhombus.
Therefore, only Statements II and IV are true. The correct answer is "II and IV only."
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A rhombus has some fascinating properties! One of its defining characteristics is that all four sides are equal in length, which gives it that distinct diamond shape. The diagonals aren’t congruent like those of a square, but they do bisect each other at right angles! In the world of geometry, rhombuses are like the quirky cousins of squares. While all squares are rhombi (hey, they have equal sides!), not all rhombi are squares. This means a rhombus can look a bit more relaxed, with angles that aren’t necessarily 90 degrees, adding to its charm!
