Question

which of the following statements is false?
select one:
a. a rectangle is a square
b. a parallelogram is a quadrilateral
c. a rectangle is a parallelogram

if in quadrilateral abcd, ab = dc and bc = da, then diagonals ac and bd
select one:
a. are equal
b. are perpendicular to each other
c. bisect each other

Explanation:

Step1: Analyze first question statements

• Statement a: A rectangle has four right angles, but only has all sides equal if it is a square. Most rectangles have unequal length and width, so this is false.
• Statement b: A parallelogram is a 4-sided figure, so it is a quadrilateral (true).
• Statement c: A rectangle has two pairs of parallel sides, so it is a parallelogram (true).

Step2: Analyze second question properties

Given $AB=DC$ and $BC=DA$, quadrilateral $ABCD$ is a parallelogram (opposite sides equal).

• Property a: Diagonals are equal only in rectangles/squares, not all parallelograms (false for general case).
• Property b: Diagonals are perpendicular only in rhombuses/squares, not all parallelograms (false for general case).
• Property c: A defining property of all parallelograms is that diagonals bisect each other (true).

Answer:

1. a. A rectangle is a square
2. c. bisect each other