Question
Use the diagram shown.
There are two horizontal parallel lines c and d which intersected by two parallel lines a and b. Line a and c makes angle 1 at left side of a and down to c. Line b and c makes angle 2 at left side of a and down to c. Line a and d makes angle 3 at left side of a and down to d.
If ∠1 ≅ ∠3, which conclusion can be made?
A. a ∥ b
B. c ∥ d
C. c ⊥ a
D. b ⊥ d
There are two horizontal parallel lines c and d which intersected by two parallel lines a and b. Line a and c makes angle 1 at left side of a and down to c. Line b and c makes angle 2 at left side of a and down to c. Line a and d makes angle 3 at left side of a and down to d.
If ∠1 ≅ ∠3, which conclusion can be made?
A. a ∥ b
B. c ∥ d
C. c ⊥ a
D. b ⊥ d
Answers
GPT-4o mini
Given that ∠1 ≅ ∠3, we can analyze the relationships between the lines in the diagram.
Since ∠1 is the angle formed between lines a and c, and ∠3 is the angle formed between lines a and d, and given that these angles are congruent, we can conclude that lines c and d are parallel.
This is because if a transversal (line a) cuts two lines (c and d) such that the alternate interior angles (∠1 and ∠3) are congruent, then the two lines being crossed (c and d) must be parallel.
Thus the conclusion that can be made is:
**B. c ∥ d**.
Since ∠1 is the angle formed between lines a and c, and ∠3 is the angle formed between lines a and d, and given that these angles are congruent, we can conclude that lines c and d are parallel.
This is because if a transversal (line a) cuts two lines (c and d) such that the alternate interior angles (∠1 and ∠3) are congruent, then the two lines being crossed (c and d) must be parallel.
Thus the conclusion that can be made is:
**B. c ∥ d**.