Examples of how to construct a parallelogram given specific properties

📚 Quick Study Guide

• 📐 Definition: A parallelogram is a quadrilateral with two pairs of parallel sides.
• 📏 Opposite Sides: Opposite sides of a parallelogram are equal in length.
• Opposite Angles: Opposite angles of a parallelogram are equal.
• ➕ Adjacent Angles: Adjacent angles of a parallelogram are supplementary (add up to 180°).
• ➗ Diagonals: The diagonals of a parallelogram bisect each other.
• 💡 Construction Methods:
  • By knowing two adjacent sides and the included angle.
  • By knowing two adjacent sides and a diagonal.
  • By knowing the lengths of both diagonals and the angle between them.
• 📐 Area: The area of a parallelogram is given by $A = b \times h$, where $b$ is the base and $h$ is the height.
• ✨ Perimeter: The perimeter of a parallelogram is given by $P = 2(a + b)$, where $a$ and $b$ are the lengths of the adjacent sides.

✏️ Practice Quiz

1. Question 1: If two adjacent sides of a parallelogram are 6 cm and 8 cm, and the included angle is 60°, which information is directly used to construct the parallelogram?
   1. Only the side lengths.
   2. Only the angle.
   3. The side lengths and the angle.
   4. None of the above.
2. Question 2: You're given two adjacent sides of a parallelogram and one of its diagonals. What construction method would you use?
   1. Using a compass and straightedge to create triangles.
   2. Measuring angles with a protractor.
   3. Calculating the area first.
   4. Guessing the shape.
3. Question 3: The diagonals of a parallelogram ABCD intersect at point E. If AE = 5 cm and BE = 4 cm, what are the lengths of AC and BD?
   1. AC = 5 cm, BD = 4 cm
   2. AC = 10 cm, BD = 8 cm
   3. AC = 4 cm, BD = 5 cm
   4. AC = 2.5 cm, BD = 2 cm
4. Question 4: Which of the following is NOT a property used in constructing a parallelogram?
   1. Opposite sides are parallel.
   2. All angles are equal.
   3. Diagonals bisect each other.
   4. Opposite sides are equal.
5. Question 5: If you know the lengths of both diagonals of a parallelogram and the angle at which they intersect, how would you begin constructing it?
   1. Draw the sides first.
   2. Draw the diagonals first.
   3. Calculate the area first.
   4. It's impossible to construct with this information.
6. Question 6: Two adjacent angles in a parallelogram are $x$ and $2x$. What are their measures?
   1. 30° and 60°
   2. 45° and 90°
   3. 60° and 120°
   4. 90° and 180°
7. Question 7: You are given two sides (a & b) and the height (h) of the parallelogram. Which of the following formulas will give you the area?
   1. a * b
   2. 2(a+b)
   3. b * h
   4. a * h