Parallel Lines
Question 4 - Find the parallel lines
Given - the angles marked in the diagram:
Line a with transversal e: 70°
Line c with transversal e: 110°
Line d with transversal f: 110°
Line c with transversal f: 70°
Reminder - When are lines parallel?
- Co-interior (same-side interior) angles that sum to 180° → lines are parallel
- Corresponding angles are equal → lines are parallel
- Alternate interior angles are equal → lines are parallel
a. Find the horizontal parallel lines:
Hint: Check which lines form co-interior angles that sum to 180°
The parallel lines are:
✓ Correct!
Explanation:
• Line a with line c: 70° + 110° = 180° → a ∥ c
• Line c with line d: 70° + 110° = 180° → c ∥ d
• Therefore: a ∥ c ∥ d
• Line a with line c: 70° + 110° = 180° → a ∥ c
• Line c with line d: 70° + 110° = 180° → c ∥ d
• Therefore: a ∥ c ∥ d
b. Find the diagonal (transversal) parallel lines:
Hint: Check the angles that lines e and f form with line c
The parallel lines are:
✓ Correct!
Explanation:
• Line e forms with c an angle of 110°
• Line f forms with c an angle of 70°
• 110° + 70° = 180° → e ∥ f
• Line e forms with c an angle of 110°
• Line f forms with c an angle of 70°
• 110° + 70° = 180° → e ∥ f