Given: segment AB || segment DE, C is the midpoint of segment DB. Prove: ΔACB ≅ ΔECD Fill in the missing reason for the proof. A
) definition of midpoint B) vertical angles are congruent C) all right angles are congruent D) supplementary angles are congruent
2 answers:
Answer:
Given: Segment AB || segment DE, C is the midpoint of segment DB.
Prove: ΔA CB ≅ ΔE CD
Proof: In ΔA CB and ΔE CD
C is the Mid point of B D.
BC=C D→ definition of midpoint
∠A CB= ∠ EC D→→vertical angles are congruent
∠BAC=∠DEC→→[AB║DE,so alternate angles are equal]
→→ΔA CB ≅ ΔE CD[A AS or A SA]
Option B: vertical angles are congruent
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Step-by-step explanation:
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Work Shown:
You could expand terms out and simplify, but I think it's more handy to leave it in this form so you can easily spot the center and radius from a glance.