Question

Parallelogram ABCD is a rectangle. Which statements are true? Select each correct answer.

a. AC=AB
b. AB⊥BC
c. AC⊥BD

Answer 1

In a rectangle ABCD, it is true that AB is perpendicular to BC (AB⊥BC), but AC is not necessarily equal to AB nor is AC necessarily perpendicular to BD.

Step-by-step explanation:

Given that parallelogram ABCD is a rectangle, we can make certain assertions about its properties:

• AB⊥BC: This statement is true because in a rectangle, consecutive sides are perpendicular to each other.
• AC⊥BD: This statement is not necessarily true. While diagonals of a rectangle are congruent, they are not necessarily perpendicular unless the rectangle is also a square.
• AC=AB: This statement is false because in a rectangle, opposite sides are equal but not necessarily the diagonals. Therefore, the diagonal AC is not equal to the side AB unless ABCD is also a square.