SME
Grade 10 Math · Problem type
Are the lines parallel?
Use this for “m∠1 = 81° and m∠5 = 79°. Are lines ℓ and m parallel?”
Diagram
Corresponding angles 1 and 5: ∠1 = 81°, ∠5 = 79°.
∠1 = 81° but ∠5 = 79°: corresponding angles differ, so the lines are not parallel.
m∠1 = 81°
m∠5 = 79°
This is an example. Type your own values to start a new problem.
m∠1
°
m∠5
°
d
Difference
calculated · °
Formulas
d
=
m∠5
−
m∠1
−2 = 79 − 81
g
:
compare
m∠1
with
m∠5
81 > 79, so not parallel
Assumptions
•
Converse: if corresponding angles are congruent, the lines are parallel.
•
If they differ, the lines meet: they cross at an angle equal to the difference.
Step-by-step
WE KNOW
m∠1 = 81°, m∠5 = 79°
FIND
difference (d), whether ℓ ∥ m (g)
Step 1 · Find difference (d)
Use d = m∠5 − m∠1
The tilt between the lines: 0° only when they are parallel.
d
=
79
−
81
d
=
−2°
Step 2 · Find whether ℓ ∥ m (g)
Use g: compare m∠1 with m∠5
m∠1 ≠ m∠5: the corresponding angles are not congruent, so ℓ and m are not parallel.
81 > 79: not parallel
g
=
compare
81
with
79
g
:
>
Check
Put the numbers back in. Both sides should match.
−2 = 79 − 81 ✓
81 > 79, so not parallel ✓
Topic check
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