6-2 Properties of Parallelograms
Objectives
To use relationships among sides and angles of parallelograms
To use relationships among diagonals of parallelograms
Lesson Vocabulary
- parallelogram
- opposite sides
- opposite angles
- consecutive angles
A parallelogram is a quadrilateral with both pairs of opposite sides parallel. In the Solve It, you made some conjectures about the characteristics of a parallelogram. In this lesson, you will verify whether your conjectures are correct.
Essential Understanding Parallelograms have special properties regarding their sides, angles, and diagonals.
In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side.
You can abbreviate parallelogram with the symbol
. You can use what you know about parallel lines and transversals to prove some theorems about parallelograms.
Take note Theorem 6-3
Theorem
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
If …
ABCD is a
Then …
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs