Answer: We can find out the missing statement with help of below explanation.
Step-by-step explanation:
We have a rectangle ABCD with diagonals AC and BD ( shown in given figure.)
We have to prove: Diagonals AC and BD bisect each other.
In triangles, AED and BEC.
[tex]\angle ADB \cong \angle CBD[/tex] ( By alternative angle theorem)
[tex]AD\cong BC[/tex] ( Because ABCD is a rectangle)
[tex]\angle CAD\cong \angle ACB[/tex] ( By alternative angle theorem)
By ASA postulate,[tex]\triangle AED\cong \triangle BEC[/tex]
By CPCTC, [tex]BE\cong ED[/tex] and [tex]CE\cong EA[/tex]
⇒ BE= ED and CE=EA
By the definition of bisector, AC and BD bisect each other.
Answer:
To Prove the diagonals of the rectangle bisect each other, Statement with reason is given:
Statement ABCD is a rectangle.
Reason:Given
Statement
:Opposite sides are parallel.(AB║DC)
Reason: Definition of a Parallelogram
Statement
:Opposite sides are parallel.(AD║BC)
Reason: Definition of a Parallelogram
Statement
:∠CAB ≅ ∠ ACB
Reason: Alternate interior angles theorem
Statement
: ∠ADB ≅ ∠CBD
Reason: Alternate interior angles theorem
Option D:∠CAB ≅ ∠ ACB
In ΔAED and ΔBEC
∠CAB ≅ ∠ ACB→→Alternate interior angle,as AB║DC.
∠ADB ≅ ∠CBD→→Alternate interior angle,as AD║BC.
AD=BC→→Opposite sides in a rectangle are equal.
ΔAED ≅ ΔBEC⇒⇒[ASA]
AE=EC→[CPCTC]
BE=ED→[CPCTC]
