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11.5 Chapter summary

  • A triangle is a polygon with three straight sides and three interior angles.
  • The sum of the interior angles of a triangle is equal to \(180^{\circ}\).
  • A scalene triangle has no equal sides. All sides are different lengths and all angles are different sizes.
  • An isosceles triangle has two equal sides. The two angles opposite the equal sides are also equal.
  • An equilateral triangle has three equal sides. All three sides are the same length and all three interior angles are equal to \(60^{\circ}\).
  • An acute-angled triangle has all interior angles less than \(90^{\circ}\).
  • A right-angled triangle has one interior angle equal to \(90^{\circ}\). The side opposite the right angle is called the hypotenuse and it is the longest side of the triangle.
  • An obtuse-angled triangle has one interior angle greater than \(90^{\circ}\) and less than \(180^{\circ}\).
  • The exterior angle of a triangle is equal to the sum of the two interior opposite angles.
  • A quadrilateral is a four-sided polygon.
  • The sum of the interior angles of a quadrilateral is \(360^{\circ}\).
  • A parallelogram is a quadrilateral with both pairs of opposite sides equal and parallel.
  • A rectangle is quadrilateral with opposites equal and parallel and interior angles equal to \(90^{\circ}\).
  • A square is parallelogram with all sides equal and interior angles equal to \(90^{\circ}\).
  • A rhombus is a quadrilateral with both pairs of opposite sides parallel and all sides equal. Two pairs of opposite angles are equal.
  • A trapezium is a quadrilateral with one pair of opposite sides parallel.
  • A kite is a quadrilateral with two pairs of adjacent sides equal.
  • Two shapes are congruent if they are the same shape and size.
  • Two shapes are similar if they are the same shape, but they may be different sizes.
  • Two shapes are similar if corresponding angles are equal and corresponding sides are in the same proportion.