Answer:
Given : A rectangle A B CD
To Prove: Diagonals of the rectangle bisect each other
Proof:
1. ABCD is a rectangle.
→AB ║CD→ Definition of a Parallelogram
→AD║BC→ Definition of a Parallelogram
⇒∠CAD ≅ ∠ACB →→[Alternate interior angles theorem]
⇒Line segment BC ≅ Line segment DA→→Definition of a Parallelogram
In Δ A DE and Δ C BE
AD=BC⇒Proved above
∠CAD=∠ACB ⇒Alternate interior angles theorem
∠ADB=∠CBE ⇒Alternate interior angles theorem
→→Δ A DE ≅ Δ C BE⇒Angle-Side-Angle (A S A) Postulate
BE=DE→→[C P CT ]
A E=CE→→[C P CT ]
⇒Line segment AC bisects Line segment B D⇒Definition of a bisector
Blank Space : Option A⇒∠ADB ≅ ∠CBD
