Each step of the proof are:
- a || b
- ∠1 ≅ ∠5
- ∠1 ≅ ∠5
- ∠5 ≅ ∠7
- ∠5 ≅ ∠7
- ∠1 ≅ ∠7
- ∠1 ≅ ∠7
How to complete the proof?
The given parameter is:
Lines a and b are parallel.
This is represented as; a || b
Corresponding angles are equal.
∠1 and ∠5 are corresponding angles.
So, we have: ∠1 ≅ ∠5
Also, they are congruent.
So, we have ∠1 ≅ ∠5
Vertical angles are equal.
∠5 and ∠7 are vertical angles.
So, we have: ∠5 ≅ ∠7
Also, they are congruent.
So, we have ∠5 ≅ ∠7
According to the transitive property;
If ∠1 ≅ ∠5 and ∠5 ≅ ∠7, then ∠1 ≅ ∠7
Hence, it has been proved that ∠1 ≅ ∠7
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