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Perpendicular & parallel lines

Basic shapes

Japanese school year: Elementary 4

What you learn

Learn the properties and construction of perpendicular lines intersecting at right angles and parallel lines that never meet on the same plane. These concepts help describe positional relationships in intersections and railroad tracks. Prior knowledge of right angles and triangle rulers ensures neat, accurate line construction.

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Key points

This formula defines perpendicular lines. When two lines ℓ and m intersect at an angle θ of 90° (a right angle), they are perpendicular.

ℓ⊥m  ⟺  θ=90∘\ell \perp m \iff \theta = 90^\circ

This equation tests if two lines ℓ and m are parallel. If the matching angles a and b are equal, the two lines are parallel.

ℓ∥m  ⟺  ∠a=∠b\ell \parallel m \iff \angle a = \angle b

This formula helps find parallel lines. If two lines ℓ and m are both perpendicular to a line n, then ℓ and m are parallel.

ℓ⊥n∧m⊥n  ⟹  ℓ∥m\ell \perp n \land m \perp n \implies \ell \parallel m

This formula shows a rule for parallel lines. If lines ℓ and n are both parallel to a third line m, then ℓ and n are also parallel.

ℓ∥m∧m∥n  ⟹  ℓ∥n\ell \parallel m \land m \parallel n \implies \ell \parallel n

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