Parallelogram Theorems Flashcards

Questions and Answers

What does the Parallelogram Opposite Sides Theorem state?

If a quadrilateral has congruent adjacent sides, then it is a parallelogram.

Opposite sides of a quadrilateral can be unequal.

All angles in a parallelogram are equal.

If a quadrilateral is a parallelogram, then it has two pairs of opposite congruent sides. (correct)

What does the Parallelogram Opposite Sides Converse Theorem state?

If the opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram. (correct)

If a quadrilateral has one pair of equal sides, it is a parallelogram.

All sides of a parallelogram are equal.

The diagonals of a parallelogram are equal.

What does the Parallelogram Opposite Angles Theorem state?

All angles in a quadrilateral are equal.

If a quadrilateral is a parallelogram, then opposite angles are congruent. (correct)

Adjacent angles in a parallelogram are equal.

The angles in a parallelogram sum to 360 degrees.

What does the Parallelogram Opposite Angles Converse Theorem state?

If two pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram. Signup and view all the answers

What does the Parallelogram Consecutive Angles Theorem state?

If a quadrilateral is a parallelogram, then the sum of consecutive angles equals 180. Signup and view all the answers

What does the Parallelogram Diagonals Theorem state?

If a quadrilateral is a parallelogram, then its diagonals bisect each other. Signup and view all the answers

What does the Parallelogram Diagonals Converse Theorem state?

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Signup and view all the answers

What is the definition of a parallelogram?

A quadrilateral with two pairs of parallel sides. Signup and view all the answers

What does the Opposite Sides Congruent and Parallel Theorem state?

If one pair of opposite sides of a quadrilateral are congruent and parallel, then the quadrilateral is a parallelogram. Signup and view all the answers

Study Notes

Parallelogram Theorems Overview

Parallelogram Opposite Sides Theorem: A quadrilateral is a parallelogram if both pairs of opposite sides are congruent.
Converse of Opposite Sides Theorem: A quadrilateral is a parallelogram if it has congruent opposite sides.

Congruent Angles in Parallelograms

Parallelogram Opposite Angles Theorem: In a parallelogram, opposite angles are congruent.
Converse of Opposite Angles Theorem: A quadrilateral is a parallelogram if its opposite angles are congruent.

Angle Relationships in Parallelograms

Parallelogram Consecutive Angles Theorem: The sum of consecutive angles in a parallelogram is always 180 degrees.

Properties of Diagonals in Parallelograms

Parallelogram Diagonals Theorem: In a parallelogram, the diagonals bisect each other.
Converse of Diagonals Theorem: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Definition and Characteristics of Parallelograms

Definition of a Parallelogram: A quadrilateral is a parallelogram if it features two sets of parallel lines.

Special Case Theorem

Opposite Sides Congruent and Parallel Theorem: If one pair of opposite sides in a quadrilateral is both congruent and parallel, then it qualifies as a parallelogram.

Description

Review essential theorems related to parallelograms with these flashcards. Learn about the properties of opposite sides and angles in parallelograms through concise definitions. Perfect for students studying geometry!