Quadrilateral Classification Notes

Quadrilaterals

  • A quadrilateral is a four-sided polygon.
  • Quadrilaterals are named using consecutive vertices.
  • The symbol for a quadrilateral is .

Names and Properties

  • Quadrilateral names: ABCD, BCDA, CDAB, DABC, DCBA, CBAD, BADC, ADCB
  • Pairs of opposite angles: ∠A and ∠C, ∠B and ∠D
  • Pairs of consecutive sides: AB and BC, BC and CD, CD and DA, DA and AB
  • Diagonals: AC and BD

Types of Quadrilaterals

  • Parallelogram: A quadrilateral with two pairs of parallel sides.
  • Rhombus: A quadrilateral with two pairs of congruent sides.
  • Rectangle: A quadrilateral with four right angles.
  • Square: A quadrilateral with four congruent angles and four congruent sides.
  • Trapezoid: A quadrilateral with exactly one pair of parallel sides.
  • Kite: A quadrilateral with two distinct pairs of consecutive sides that are congruent.

Quadrilateral Angle-Sum Theorem

  • Sum of interior angles in a quadrilateral = 360°
    • A+B+C+D=360A + B + C + D = 360
  • Sum of exterior angles in a quadrilateral = 360°

Example Problems

  • Problem 1: Find the measure of each angle indicated, given ∠Q, ∠R, and ∠S of quadrilateral QRST.
    • ∠Q + ∠R + ∠S + ∠T = 360°
    • 79° + 88° + 108° + ∠T = 360°
    • ∠T = 360° – 275°
    • ∠T = 85°

Additional Problems

These are example problems from the slides. The solutions are not available in the transcript.

  • Problem 2: Find the measure of each angle indicated in the quadrilateral.

  • Problem 3: Find the measure of each angle indicated in the quadrilateral, given angles as expressions of xx.

  • Problem 4: Find the measure of each angle indicated in the quadrilateral, given angles as expressions of xx.