Question

show that ∆AFE is congruent to ∆CBD

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Answer 1

Step-by-step explanation:

Given: ∆AEF and ∆CBD such that :

1. AB=CF
2. EF=BD
3. angle AFE=angle CBD.

To prove: ∆AEF≈ ∆CBD

proof:

Consider (1):

AB=CF

By adding BF to both sides:

AB+BF=BF+FC

: AF=BC.

Now, In ∆AEF and ∆CBD;

sides: EF=BD. (given)

Angles: angle AFE=angle CBD.( given)

sides: AF=BC ( proved above)

So,

∆AEF≈ ∆CBD.( SAS congruence rule)

Hence proved.