Question

Mary states, "If the diagonals of a parallelogramare congruent, then the

parallelogram is a rectangle." Decide if her statement is wue or false.
A. True
B. False​

Answer 1

True

Explanation:

A rectangle is a plane figure with congruent length of opposite sides. Considering a rectangle ABCD,

AD ≅ BC (opposite side property)

AB ≅ CD (opposite side property)

<ABC = <BCD = <CDA = <DAC =
`90^(0)` (right angle property)

Thus,

<ABC + <BCD + <CDA + <DAC =
`360^(0)`

AC ⊥ BD (diagonals are perpendicular to each other)

AC ≅ BD (congruent property of diagonals)

Therefore, the parallelogram is a rectangle.