20 Questions
Which of the following is sufficient to guarantee that a quadrilateral is a parallelogram?
Opposite sides are equal in length
What values of x and y guarantee that Quadrilateral ABCD is a parallelogram?
x = 640, y = 640
In the same figure above, If AD = 2x – 10 cm and BC = x + 30 cm, then BC =
70 cm
Quadrilateral ABCD is a parallelogram. If m∠B = (x + 40)° and m∠D = (2x + 20)°, what is m∠B?
60°
Quadrilateral ABCD is a parallelogram. If m∠A = (3x – 10)° and m∠D = (2x + 40)°, what is m∠A?
70°
Which of the following statements is true about parallelograms?
Any two opposite sides of a parallelogram are equal in length.
What happens if one pair of opposite sides of a quadrilateral are parallel and congruent?
It becomes a parallelogram.
What are the conditions for a quadrilateral to be classified as a parallelogram?
Only one pair of opposite sides are parallel and congruent.
In a parallelogram, what can be said about any two consecutive angles?
They add up to 180 degrees.
What is true about the naming convention of parallelograms?
The naming convention can start at any vertex in any order.
In a parallelogram, what is true about any two consecutive angles?
They are supplementary
If ̅̅̅̅ ≅ ̅̅̅ and ̅̅̅̅ // ̅̅̅ , then what can be concluded about the quadrilateral LIVE?
It is a parallelogram
What happens if one pair of opposite sides of a quadrilateral are parallel and congruent?
The quadrilateral may be a parallelogram
In a parallelogram, what can be said about the diagonals?
They bisect each other
Which of the following conditions is sufficient to guarantee that a quadrilateral is a parallelogram?
One pair of opposite sides are parallel and congruent
If m̅̅̅̅ = 13 cm, then m̅̅̅̅ = _____
3x - 5 cm
Quadrilateral ABCD is a parallelogram. If m∠A = (3x – 10)° and m∠D = (2x + 40)°, what is m∠A?
80°
What values of x and y guarantee that Quadrilateral ABCD is a parallelogram?
x = 640, y = 1160
In the same figure above, If AD = 2x – 10cm and BC = x + 30 cm, then BC =
70 cm
Which of the following is sufficient to guarantee that a quadrilateral is a parallelogram?
Opposite sides are parallel and congruent
Study Notes
Conditions for a Parallelogram
- A quadrilateral is a parallelogram if one pair of opposite sides are parallel and congruent.
- A quadrilateral is a parallelogram if both pairs of opposite angles are equal.
- A quadrilateral is a parallelogram if both pairs of opposite sides are equal.
- A quadrilateral is a parallelogram if the diagonals bisect each other.
Properties of Parallelograms
- In a parallelogram, any two consecutive angles are supplementary (add up to 180°).
- In a parallelogram, the diagonals bisect each other.
- In a parallelogram, opposite sides are equal and parallel.
Naming Convention of Parallelograms
- The naming convention of parallelograms is to name them in alphabetical order.
Consecutive Angles in Parallelograms
- In a parallelogram, any two consecutive angles are supplementary (add up to 180°).
Diagonals in Parallelograms
- In a parallelogram, the diagonals bisect each other.
Quadrilateral ABCD
- Quadrilateral ABCD is a parallelogram if AD = 2x – 10 cm and BC = x + 30 cm.
- Quadrilateral ABCD is a parallelogram if m∠A = (3x – 10)° and m∠D = (2x + 40)°.
Example Problems
- If m̅̅̅̅ ≅ ̅̅̅ and ̅̅̅̅ // ̅̅̅, then the quadrilateral LIVE is a parallelogram.
- If m̅̅̅̅ = 13 cm, then m̅̅̅̅ = ?.
Learn about the definition of a parallelogram as a quadrilateral with two pairs of parallel sides, and the rules for naming a parallelogram. Explore the properties of a parallelogram, including the congruence of opposite sides.
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