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Chapter summary

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12.7 Chapter summary

  • The sum of angles that are formed on a straight line is \(180^{\circ}\).
  • Vertically opposite angles are always equal.
  • If lines are parallel then:
    • The corresponding angles are equal. (Reason: corresp \(\angle\)s; …//… )
    • The alternate angles are equal. (Reason: alt \(\angle\)s; …//… )
    • The co-interior angles are supplementary. (Reason: co-int \(\angle\)s; …//… ).
  • Remember that you have to state which parallel lines you are using when you give the reasons above.

Statements and abbreviations for reasons

  • Angles on a straight line add up to \(180^{\circ}\) (\(\angle\)s on a str line)
  • Vertically opposite angles are equal (vert opp \(\angle\)s)
  • Angles around a point add up to \(360^{\circ}\) (\(\angle\)s around a pt)
  • Corresponding angles of parallel lines are equal (corresp \(\angle\)s ; …//… )
  • Alternate angles of parallel lines are equal (alt \(\angle\)s ; …//… )
  • Co-interior angles between parallel lines add up to \(180^{\circ}\) (co-int \(\angle\)s ; …//… )
  • The sum of the interior angles of a triangle add up to \(180^\circ\) (sum of \(\angle\)s in a \(\triangle\))
  • The exterior angle of a triangle is equal to the sum of the interior opposite angles (exterior \(\angle\) of \(\triangle\))
  • The interior angles of a quadrilateral add up to \(360^\circ\) (sum of \(\angle\)s in a quad)