Angles and parallel lines

Japanese school year: Junior high 2

What you learn

Learn the geometric properties of corresponding and alternate interior angles formed when a transversal intersects parallel lines. This knowledge is essential for calculating unknown angles and proving geometric properties. Familiarity with straight line angles and vertically opposite angles is helpful.

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Key points

This relation is used to check if two lines $\ell$ and $m$ are parallel or to find unknown angles. The lines are parallel if and only if corresponding angles or alternate interior angles $\angle a$ and $\angle b$ are equal.

\ell \parallel m \iff \angle a = \angle b

This relation is used to determine whether lines $\ell$ and $m$ are parallel. The lines are parallel if and only if the consecutive interior angles on the same side, $\angle a$ and $\angle b$ , add up to $180^\circ$ .

\ell \parallel m \iff \angle a + \angle b = 180^\circ

This formula is used to find angles where two straight lines intersect. Opposite angles (vertical angles) $\angle a$ and $\angle c$ are always equal to each other.

\angle a = \angle c

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Practice 1Coming soon