∠DAE is congruent to ∠BAE.
Given: The circle centered at point A has a radius of length AB. The circles centered at points B and D have radii of length DE.
To prove: ∠DAE ≌ ∠BAE
Proof:
AB = AD (All radii of the same circle have the same length.)
DE = AE (They're lengths of the same segment.)
AE = DE (Symmetric property of equality.)
AB = AD, DE = AE, and ∠ADE = ∠BAE (Given information.)
ΔADE ≌ ΔBAE (Side-side-side congruence - using 1, 2, and 4)
∠DAE ≌ ∠BAE (Corresponding parts of congruent triangles are congruent - using 5).
Therefore, ∠DAE is congruent to ∠BAE.
Question
The circle centered at point A has a radius of length AB. The circles centered at points B and D have radii of length DE. Complete the proof that ∠ DAE≌ ∠ BAE. Step Statement Reason 1 AB=AD All radii of the same circle have the same length. 2 Both circles have radii of the same length. AE=AE They're lengths of the same segment. 4 Side-side-side congruence (1. 2. 3) 5 ∠ DAE≌ ∠ BAE Corresponding parts of congruent triangles are congruent (5).