SME
Grade 10 Math
Parallel and perpendicular lines: transversals and proofs
The main lesson, then each kind of problem it solves.
Parallel and perpendicular lines: transversals and proofs
Main lesson
Alternate interior angles
Use this for “ℓ ∥ m and m∠1 = 118°. Find m∠3 and m∠6.”
Same-side interior angles
Use this for “ℓ ∥ m and m∠4 = 73°. Find m∠6.”
Are the lines parallel?
Use this for “m∠1 = 81° and m∠5 = 79°. Are lines ℓ and m parallel?”
Angle expressions
Use this for “ℓ ∥ m, corresponding angles are (4x + 12)° and (2x + 50)°. Find x and the angle.”
A parallel line through a point
Use this for “Write the equation of the line parallel to y = 3x − 4 through (2, 7).”
A perpendicular line through a point
Use this for “Write the equation of the line perpendicular to y = 2x + 1 through (4, 3).”
Why a triangle’s angles add to 180°
Use this for “Prove that the angles of a triangle add to 180°.”