Prove that the diagonals of a rectangle are congruent
Given a rectangle, prove that the diagonals are congruent.
: Rectangle ABCD
: segment AC ≅ segment BD
Since ABCD is a rectangle, it is also a parallelogram.
Since ABCD is a parallelogram, segment AB ≅ segment DC because opposite sides of a parallelogram are congruent
BC ≅ BC by the Reflexive Property of Congruence.
Furthermore, ∠ABC and ∠DCB are right angles by the definition of rectangle.
∠ABC ≅ ∠DCB since all right angles are congruent.
AB ≅ segment DC
∠ABC ≅ ∠DCB
BC ≅ BC
Therefore, by SAS, triangle ABC ≅ triangle DCB.
Since triangle ABC ≅ triangle DCB, segment AC ≅ segment BD
Mar 13, 19 11:50 AM
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