Theorems on Rectangles

• Rectangle


  • 4 sides
  • 4 vertices
  • 4 angles
  • Opposite sides are parallel
  • Opposite sides are congruent
  • Adjacent sides are perpendicular
• If a parallelogram has one right angle, then it has four right angles and the parallelogram is a rectangle
• Diagonals of a rectangle

  Congruent
• Finding length using rectangle ABCD

  1. Given: AC = 2x + 31, BD = 3(4x - 3)

  2. Solve for x

  3. Find measure of AC and BD
• Finding x if ABCD is a rectangle with BC = 4x - 30, AD = x


  1. Opposite sides are congruent

  2. Solve for x
• If VX = 20


  WY = 20
• Finding VP if YP + PW = 56

  1. Diagonals are congruent

  2. VX = 56

  3. VP = 1/2 of VX = 28
• Finding AC - BD if AB = 28, AD = 21


  1. Use Pythagorean theorem to find BD

  2. BD = 35

  3. AC = 35

  4. AC - BD = 0
• Finding AC and BD if EC = 25

  1. EC = 1/2 of AC

  2. AC = 50

  3. BD = 50
• Finding value of x if AC = 5x, BD = 9x - 80


  1. AC = BD (diagonals are congruent)

  2. Solve for x = 20

  3. AE = 1/2 of AC = 50