SME
Grade 10 Math · Geometry
Parallel and perpendicular lines: transversals and proofs
Use this for “Two parallel lines are cut by a transversal and m∠1 = 62°. Find the corresponding angle ∠5.”
Diagram
Corresponding angles 1 and 5: ∠1 = 62°, ∠5 = 62°, equal.
The lines are parallel (arrows): angles 1, 4, 5 and 8 are 62°; 2, 3, 6 and 7 are 118°.
m∠1 = 62°
m∠5 = 62°
This is an example. Type your own values to start a new problem.
m∠1
m∠1
example · °
m∠5
m∠5
calculated · °
Formulas
m∠5 = m∠1
62 = 62
Assumptions
•
Lines ℓ and m are parallel, and the transversal crosses both.
•
Corresponding angles sit in the same position at each crossing: 1 and 5, 2 and 6, 3 and 7, 4 and 8.
•
When the lines are parallel, corresponding angles are congruent.
Step-by-step
WE KNOW
m∠1 = 62°
FIND
m∠5 (m∠5)
Step 1 · Find m∠5 (m∠5)
Use m∠5 = m∠1
Parallel lines: corresponding angles are congruent.
m∠5 = 62°
Check
Put the numbers back in. Both sides should match.
62 = 62 ✓
Topic check
See what you know: 5 questions on this topic
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