From Parallelograms to Triangles: IM 6.1.7 LEACH
[url=https://im.kendallhunt.com/MS/teachers/1/1/7/preparation.html]“From Parallelograms to Triangles”[/url] from IM Grade 6 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson
- Copy of IM 6.1.7 Lesson: From Parallelograms to Triangles
- Practice
- Copy of IM 6.1.7 Practice: From Parallelograms to Triangles
Copy of IM 6.1.7 Lesson: From Parallelograms to Triangles
Here are two copies of a parallelogram. Each copy has one side labeled as the base b and a segment drawn for its corresponding height and labeled h.
The base of the parallelogram on the left is 2.4 centimeters; its corresponding height is 1 centimeter. Find its area in square centimeters. You can use the app to help explain.[br]
The height of the parallelogram on the right is 2 centimeters. How long is the base of that parallelogram? Explain your reasoning. You can use the app to help.
Two polygons are identical if they match up exactly when placed one on top of the other.
Draw one line to decompose each polygon into two identical triangles, if possible. If you choose to, you can also draw the triangles.
Which quadrilaterals can be decomposed into two identical triangles?
Study the quadrilaterals that were, in fact, decomposable into two identical triangles. What do you notice about them? Write a couple of observations about what these quadrilaterals have in common.
This applet has eight pairs of triangles. Each group member should choose 1–2 pairs of triangles. Use them to help you answer the following questions.
Discuss your responses to the first question with your group. Then, complete each of the following statements with [i]all[/i], [i]some[/i], or [i]none[/i]. [br][br]________________ of these pairs of identical triangles can be composed into a [i]rectangle[/i].[br]________________ of these pairs of identical triangles can be composed into a [i]parallelogram[/i].
Sketch 1–2 examples to illustrate each completed statement.
Copy of IM 6.1.7 Practice: From Parallelograms to Triangles
Select [b]all [/b]the segments that could represent the height if side [math]n[/math] is the base.[br][br][img width=327,height=224]https://lh6.googleusercontent.com/KVzNY1DPklPndNHbB7qTZf_apZqxCuugdHcZeGSJ82iub8bWYmoAeOccglK9U65MbAtx1Vt92WqsMR2hBKd6Q1faiQDtcWEyu43Ur0l0nbIsJa1SuxesPz3Lz2wrJd-Mo7yLydUs[/img]
Two copies of this triangle are used to compose a parallelogram. Which parallelogram [i]cannot[/i] be a result of the composition? If you get stuck, consider using tracing paper.[br][br][img width=251,height=158]https://lh4.googleusercontent.com/nYsR_Zk662PFNaRfRYflv3VPK8MqFCJGWypivfG8NfOUwIFJ9NuWMz4rPm9Gl04MKR7eNDQ1Fvl2xAS8rqwjF4gqB3pwpiot93Twjsq5RYHiOUJo3erTONeONzLY2PZGtdhCIxqX[/img] [img width=331,height=159]https://lh5.googleusercontent.com/Q2cqrx6V0j2ELiaN5bLeihOl-_9vNgnj42VzkvAWaJ--l6SGiFEYbnYxBs0bg_LSRfmmG-ZEy81GdlivixzOcFHQsSV_vue_0VS44UIps2tPl_mlQMY76DgaFZJKGBjMsMTfkPG-[/img]
Triangle R is a right triangle. Can we use two copies of Triangle R to compose a parallelogram that is not a square?[br][br][img width=269,height=134]https://lh6.googleusercontent.com/gne-F2wEsH401BsBhgCdIOp1tt5tjRgqbzjI0KvrphMJjMds0CiZqMeCEy1P0GbCHYMPVwjDRHNlb-oSZXjxNPzeB9fayf1zJlEGbEkV4ddKysRpeCo5d1O3DNtrfga57bIKXj12[/img][br][br]If so, explain how. If not, explain why not.
A parallelogram has a base of 9 units and a corresponding height of [math]\frac{2}{3}[/math] units. What is its area?
A parallelogram has a base of 9 units and an area of 12 square units. What is the corresponding height for that base?
A parallelogram has an area of 7 square units. If the height that corresponds to a base is [math]\frac{1}{4}[/math] unit, what is the base?