Quadrilateral RUBY is a rectangle.
Which of the following statements MUST be true?
Check all that apply:
[] All four of the sides of RUBY are equal.
[]All four of the angles of RUBY are equal.
[]RUBY has two pairs of parallel opposite sides.
One is not true. Which two statements are true?
2 and 3
The following statements must be true:
[X] RUBY has two pairs of parallel opposite sides.
[] All four of the sides of RUBY are equal.
[] All four of the angles of RUBY are equal.
To determine which statements must be true, we need to understand the properties of a rectangle.
A rectangle is a quadrilateral with several key properties:
1. All four angles are right angles (90 degrees).
2. Opposite sides are parallel.
3. Opposite sides are equal in length.
Given that Quadrilateral RUBY is a rectangle, we can conclude the following:
- All four of the angles of RUBY are equal (90 degrees). This is because all angles in a rectangle are right angles. Therefore, the statement "All four of the angles of RUBY are equal" must be true.
- RUBY has two pairs of parallel opposite sides. This is because all opposite sides of a rectangle are parallel. Therefore, the statement "RUBY has two pairs of parallel opposite sides" must be true.
On the other hand, we cannot say that "All four of the sides of RUBY are equal" must be true. While opposite sides are equal in length, adjacent sides of a rectangle may have different lengths.
In conclusion, the following statements MUST be true for Quadrilateral RUBY to be a rectangle:
- All four of the angles of RUBY are equal.
- RUBY has two pairs of parallel opposite sides.