Practical Examples of Using Quadrilateral Properties

📚 Quick Study Guide

• ✅ Quadrilateral Definition: A closed, two-dimensional shape with four straight sides.
• ✅ Parallelogram Properties:
  • Opposite sides are parallel and congruent.
  • Opposite angles are congruent.
  • Consecutive angles are supplementary (add up to 180 degrees).
  • Diagonals bisect each other.
• ✅ Rectangle Properties:
  • All properties of a parallelogram.
  • All four angles are right angles (90 degrees).
  • Diagonals are congruent.
• ✅ Square Properties:
  • All properties of a parallelogram, rectangle, and rhombus.
  • All four sides are congruent.
  • All four angles are right angles (90 degrees).
  • Diagonals are congruent and perpendicular bisectors of each other.
• ✅ Rhombus Properties:
  • All properties of a parallelogram.
  • All four sides are congruent.
  • Diagonals are perpendicular bisectors of each other.
  • Diagonals bisect the angles.
• ✅ Trapezoid Properties:
  • Only one pair of opposite sides are parallel (called bases).
• ✅ Isosceles Trapezoid Properties:
  • One pair of opposite sides are parallel (bases).
  • The non-parallel sides (legs) are congruent.
  • Base angles are congruent.
  • Diagonals are congruent.

🧪 Practice Quiz

1. Question 1: In parallelogram $ABCD$, if angle $A = 60$ degrees, what is the measure of angle $C$?
   1. A) 30 degrees
   2. B) 60 degrees
   3. C) 120 degrees
   4. D) 90 degrees
2. Question 2: Which property is unique to a rectangle compared to a general parallelogram?
   1. A) Opposite sides are congruent.
   2. B) Diagonals bisect each other.
   3. C) All angles are right angles.
   4. D) Opposite angles are congruent.
3. Question 3: In rhombus $PQRS$, if diagonal $PR$ bisects angle $P$, what is the relationship between the sides $PQ$ and $QR$?
   1. A) $PQ > QR$
   2. B) $PQ < QR$
   3. C) $PQ = QR$
   4. D) They are perpendicular.
4. Question 4: In square $WXYZ$, what is the angle formed by the intersection of the diagonals?
   1. A) 30 degrees
   2. B) 45 degrees
   3. C) 60 degrees
   4. D) 90 degrees
5. Question 5: In trapezoid $EFGH$, sides $EF$ and $GH$ are parallel. If angle $E = 70$ degrees, and angle $G = 110$ degrees, what type of trapezoid is it?
   1. A) Isosceles trapezoid
   2. B) Right trapezoid
   3. C) Scalene trapezoid
   4. D) It cannot be determined.
6. Question 6: Which quadrilateral always has congruent diagonals?
   1. A) Parallelogram
   2. B) Rhombus
   3. C) Trapezoid
   4. D) Rectangle
7. Question 7: If a quadrilateral has one pair of parallel sides and the other pair of sides are congruent, what is the most precise name for the shape?
   1. A) Parallelogram
   2. B) Trapezoid
   3. C) Isosceles Trapezoid
   4. D) Rectangle