Geometry: Properties of Parallelograms

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Questions and Answers

What can be concluded about the angles of a parallelogram based on the exploration?

  • All angles measure 90°.
  • Opposite angles are supplementary.
  • Opposite angles are the same. (correct)
  • Consecutive angles are equal.

What do the diagonals of a parallelogram do?

  • They are always equal in length.
  • They never intersect.
  • They create right angles.
  • They bisect each other. (correct)

What is a property of the sides of a parallelogram?

  • Opposite sides are congruent. (correct)
  • All sides are equal.
  • Adjacent sides are equal.
  • All sides are parallel.

Which angle measures were observed in the parallelogram?

<p>Two angles measure 68.2° and two measure 111.8°. (B)</p> Signup and view all the answers

What is true regarding the lengths of the sides of the parallelogram?

<p>Adjacent sides can have different lengths. (D)</p> Signup and view all the answers

What defines a polygon?

<p>A two-dimensional closed figure with sides that are segments. (B)</p> Signup and view all the answers

What is true about equilateral polygons?

<p>All sides are congruent. (D)</p> Signup and view all the answers

What does the Triangle Exterior Angle Theorem state?

<p>The exterior angle equals the sum of its two remote interior angles. (C)</p> Signup and view all the answers

Which of the following correctly describes an exterior angle of a polygon?

<p>An angle on the outside of a polygon that forms a linear pair with an interior angle. (C)</p> Signup and view all the answers

Which statement about regular polygons is true?

<p>They have all sides and all angles congruent. (D)</p> Signup and view all the answers

What is one method to prove that a quadrilateral is a parallelogram?

<p>Show that both pairs of opposite sides are congruent. (B)</p> Signup and view all the answers

Which of the following pairs of slopes correctly demonstrates that two sides are parallel?

<p>Both sides have a slope of $ rac{2}{3}$. (A)</p> Signup and view all the answers

If two pairs of opposite angles in a quadrilateral are congruent, what can be concluded?

<p>It is a parallelogram. (C)</p> Signup and view all the answers

Which statement best describes the relationship necessary for diagonals to prove a quadrilateral is a parallelogram?

<p>The diagonals must bisect each other. (B)</p> Signup and view all the answers

To determine if quadrilateral STUV is a parallelogram using the first method, what key condition was met?

<p>Both pairs of opposite sides are parallel. (B)</p> Signup and view all the answers

Flashcards

Parallelogram Definition

A quadrilateral is a parallelogram if both pairs of opposite sides are parallel.

Parallelogram Opposite Sides Converse

A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.

Parallelogram Opposite Angles Converse

A quadrilateral is a parallelogram if both pairs of opposite angles are congruent.

Opposite Sides Parallel and Congruent Theorem

A quadrilateral is a parallelogram if one pair of opposite sides are congruent and parallel.

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Parallelogram Diagonals Converse

A quadrilateral is a parallelogram if the diagonals bisect each other.

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Polygon

A two-dimensional closed figure with sides that are segments.

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Interior Angle

An angle formed by two consecutive sides of a polygon on the inside of the polygon.

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Exterior Angle

An angle on the outside of a polygon that forms a linear pair with an interior angle.

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Equilateral Polygon

A polygon where all sides have the same length.

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Triangle Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of its two remote interior angles.

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Opposite angles in a parallelogram are congruent

Opposite angles in a parallelogram are equal in measure.

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Consecutive angles in a parallelogram are supplementary

Consecutive angles in a parallelogram are supplementary, meaning they add up to 180 degrees.

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Diagonals of a parallelogram bisect each other

The diagonals of a parallelogram bisect each other. This means they cut each other in half at their point of intersection.

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Diagonals of a parallelogram create four congruent triangles

The diagonals of a parallelogram divide the parallelogram into four congruent triangles.

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Diagonals of a parallelogram create congruent alternate interior angles

The diagonals of a parallelogram create alternate interior angles that are congruent. This means that the angles formed on opposite sides of the diagonal are equal in measure.

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