Theorems of Rhombus

• Rhombus


  • All four sides are congruent
  • Opposite angles are congruent
  • Diagonals bisect each other
  • Diagonals are perpendicular
  • Diagonals bisect vertices
  • Consecutive angles are supplementary
• Solving problems involving rhombus

  1. Find the measure of angle CEA

  2. Find the measure of angle ACE

  3. Find the measure of angle ECR

  4. Find the measure of angle CRE
• Parallelogram CARE is a rhombus
• Measure of angle CAR is 96 degrees
• Opposite angles


  Congruent
• Angle CAR is 96 degrees


  Angle CEA is 48 degrees
• Angle CAR is 96 degrees


  Angle ACE is 84 degrees
• Angle ECR


  Half of angle ACE, which is 42 degrees
• Angle CRE


  Equal to angle ECR, which is 42 degrees
• Finding the measure of each numbered angle in the rhombus

  1. Angle 1 is 54 degrees

  2. Angle 5 is 54 degrees

  3. Angle 2 is 54 degrees

  4. Angle 3 is 54 degrees
• Diagonals of a rhombus bisect opposite angles
• Diagonals of a rhombus are not congruent
• Diagonals of a rhombus are perpendicular
• Diagonals of a rhombus bisect vertices
• Consecutive angles in a rhombus are supplementary
• Opposite sides of a rhombus are congruent
• Measure of angle NAL is 124 degrees
• Measure of angle CNL is 28 degrees
• Measure of angle 2 is 90 degrees
• Measure of angle 3 is 100 degrees
• Measure of angle 4 is 50 degrees