IM 6.1.5 Lesson: Bases and Heights of Parallelograms - Activities 1-3

Tyler was trying to find the area of this parallelogram. Move the slider to see how he did it.

Elena was also trying to find the height of this parallelogram. Move the slider to see how she did it.

How are the two strategies for finding the area of a parallelogram the same? How they are different?

Study the examples and non-examples of [b]bases[/b] and [b]heights[/b][color=#0c0300] of parallelograms.[br][/color][list][*]Examples: The dashed segments in these drawings represent the corresponding height for the given base.[/*][/list][br][center][img width=315,height=247]https://lh3.googleusercontent.com/9q2HsRJttm9IFRcc2xJFUDSRcxwY9_yFf8hz1YIy9GhZWt1txhDi4yUZz1_ydiyORzOdYCf0qpAPeYCV6ZaX485rU_L7s0ieaTJewTOTVlwddX_4KgJG9fkvX8WbqPZXZjpxc3Ub[/img][/center][br][list][*]Non-examples: The dashed segments in these drawings do [i]not[/i] represent the corresponding height for the given base.[/*][/list][center][img width=318,height=251]https://lh4.googleusercontent.com/E_zlbivvcppz-GQHnQfcnHa64Gh3l2hbaTbQg_cRmuXcnFzPOA3FhWSB5yR9nAUky9CRQ7l7n6ukSTCtoueZzsm2j4FHSFwp0CYyo0XicvU31Q3Q8bXqEVEFJUBhmzqF4tRHWOCl[/img][/center]

Select all the statements that are true about bases and heights in a parallelogram.

A base cannot be extended to meet a height.[br] A height can be drawn at any angle to the side chosen as the base.[br] Only a horizontal side of a parallelogram can be a base. A height can be drawn outside of the parallelogram, as long as it is drawn at a 90-degree angle to the base.[br] A height can only be drawn inside a parallelogram.[br] Any side of a parallelogram can be a base.[br] A base and its corresponding height must be perpendicular to each other.[br]

Five students labeled a base [i]b[/i] and a corresponding height [i]h[/i] for each of these parallelograms. [br][br][img width=458,height=268]https://lh6.googleusercontent.com/dstBy0HSNeckUxaHb4pc8CgReTGS4RjqF6hLd0cs4wM0KbZEUKMSgBo_rb_jO8ZlPGyIhh6KxboctQ23dN1t4E0f7AiYhZKvNmSuFMPywzabt6WiiWPQL_oLBMteMaV4RqeWY7FJ[/img][br][br]Which drawings are correctly labeled? Check all that apply:

D A C B E

[br][img width=458,height=268]https://lh6.googleusercontent.com/dstBy0HSNeckUxaHb4pc8CgReTGS4RjqF6hLd0cs4wM0KbZEUKMSgBo_rb_jO8ZlPGyIhh6KxboctQ23dN1t4E0f7AiYhZKvNmSuFMPywzabt6WiiWPQL_oLBMteMaV4RqeWY7FJ[/img][br][br]For each item you selected above, explain how you know why the these setups you selected above are correct.

This parallelogram is made of solid line segments. Its height and supporting lines are dashed. Interact with this, and answer the questions that follow.

For each parallelogram here, use the SEGMENT tool to construct its base and height. Drag a label next to each segment to denote which is which for each.

For the parallelograms above, record these lengths in the table below. In the last row, write an expression (using b and h) for the area of any parallelogram.