Prove that diagonals of a rectangle are congruent. ABCD is a rectangle

texelaare

texelaare

Answered question

2021-07-27

To prove : 
The diagonals of a rectangle are equal in length.
Given information: 
ABCD is a rectangle.

Answer & Explanation

Obiajulu

Obiajulu

Skilled2021-07-28Added 98 answers

Concept used:
Here, we are using the concept of Side Angle side congruency.
Proof:
image

Since ABCD is a rectangle, it is also a parallelogram.
AB=DC (because opposite sides of a parallelogram are congruent)
BC=BC (by reflexive property of congruence)
ABC=DCB (since all right angles are congruent)
ABC=DCB (by Side Angle Side congruency)
Hence, AC=BD (by corresponding parts of congruent triangles)

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