Investigate Parallelograms

Question:

What are some of the properties of parallelograms?

Explore: Draw a quadrilateral.

1. Using the Line Tool, draw line AB. 2. Through point C, (C not on line AB) draw a second line, parallel to AB. 3. Construct line BC, then construct a line parallel to BC through point A. 4. Use the Intersect Tool under Points to construct the intersection of all lines drawn in steps 1 - 3. Intersection points A, B, and C have already been labeled. Label the 4th intersection point D. 5. Now use the segment tool to construct segments AB, BC, CD, and DA. 6. Hide all lines. This leaves quadrilateral ABCD Measuring Side Lengths and Angles: Drag vertex A, or B, or C to change the side lengths of ABCD. What do you notice about the side lengths? What do you notice about the angle measures?

Relationship between pairs of opposite sides

As you drag a vertex, do the pairs of opposite sides remain congruent?

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Relationship between pairs of opposite angles

As you drag a vertex, do the pairs of opposite angles remain congruent?

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Definition of a Parallelogram

Based on your observations in connection to the interior angles of the quadrilateral, which of the following postulates or theorems could you directly use to prove that the opposite sides are parallel?

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Proving a quadrilateral is a parallelogram

In the diagram, segment AB is extended past point B. Which postulate(s) or theorem(s) could you use to prove that the quadrilateral is a parallelogram? (Select all that apply.)

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