Identify properties of parallelograms

A parallelogram is a four-sided figure in which both pairs of opposite sides are parallel; its opposite sides have equal lengths, and its opposite angles have equal measures. This understanding includes rectangles, rhombuses, and squares as special parallelograms while distinguishing them from figures that merely have four sides or one pair of parallel sides, supporting later classification and angle reasoning in geometry.

Detailed Explanation: Identify properties of parallelograms

A parallelogram is a four-sided figure with two pairs of opposite sides parallel.

Opposite sides are across from each other.
The opposite sides also have equal lengths.
Opposite angles have equal measures.
Rectangles, rhombuses, and squares are special types of parallelograms.

Worked example

Problem: Quadrilateral $(ABCD)$ has these properties:

AB \parallel CD

BC \parallel AD

Also,

AB=CD=6\text{ cm}

and

BC=AD=4\text{ cm}.

Is $(ABCD)$ a parallelogram?

Step 1: Check the first pair of opposite sides.

Side $(AB)$ is opposite side $(CD)$ . Since

AB \parallel CD,

the first pair is parallel.

Step 2: Check the second pair of opposite sides.

Side $(BC)$ is opposite side $(AD)$ . Since

BC \parallel AD,

the second pair is parallel.

Step 3: Decide.

Both pairs of opposite sides are parallel, so $(ABCD)$ is a parallelogram.

The equal lengths confirm the pattern:

AB=CD \quad\text{and}\quad BC=AD.

Remember: A shape is not a parallelogram just because it has four sides. It must have both pairs of opposite sides parallel.

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Quadrilaterals - Is Shape of a Type

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