{"id":346,"date":"2018-01-08T04:39:26","date_gmt":"2018-01-08T04:39:26","guid":{"rendered":"https:\/\/www.primefactorisation.com\/blog\/?p=346"},"modified":"2024-11-02T15:02:43","modified_gmt":"2024-11-02T20:02:43","slug":"parallelogram-and-rhombus-theorems","status":"publish","type":"post","link":"https:\/\/www.primefactorisation.com\/blog\/2018\/01\/08\/parallelogram-and-rhombus-theorems\/","title":{"rendered":"Parallelogram and Rhombus Theorems"},"content":{"rendered":"

First day back from Christmas break saw my Geometry classes looking at theorems about parallelograms and rhombuses. We’d already looked at definitions of the different types of special quadrilaterals. I had students divide a page in their notebook in two, and told them to rewrite the definitions of the parallelogram and rhombus in those sections.<\/p>\n

While they were doing that, I passed out a set of four Exploragons to each student, with two each of two different colors\/lengths. I also made sure that each pair of students received the same colors, which will be important later.<\/p>\n

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If you haven’t used Exploragons before, they’re plastic sticks with little nubs that allow the sticks to snap together to make different geometric arrangements. Other companies sell them as AngLegs, though I think prefer Exploragons as they have nubs in the middle of the sticks, not just at the ends. When I started teaching at Drumright, I had the opportunity to order hands-on supplies to use. I’ve found that of everything I’ve ordered, these are the most versatile physical tool I have for teaching Geometry.<\/p>\n

I gave students the instruction to construct a parallelogram from the pieces I gave them. Thankfully, they (mostly) ended up with something like these:<\/p>\n

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I then instructed them to write down everything they noticed about their shapes, and to discuss what they notice with the students around them. Answers ranged from what I was hoping they’d notice (opposite angles are the same, opposite sides are the same length) to not as useful (“it’s a shape”), but getting the perfect answer wasn’t really the point. I wanted students to understand that there are things about these quadrilaterals we can know are true aside from just their definitions.<\/p>\n

Next, I told students to do the same thing by making a rhombus. Thankfully, they realized I didn’t have the right pieces to do this A few looked at me incredulously, a few demanded I give them more pieces (which I refused), but slowly a few students worked out what they needed to do: trade pieces with the person next to them.<\/p>\n

Once students had had time to write down their observations of their rhombus, we started our notes summarizing the theorems for these quadrilaterals. I used the observations as a springboard into this conversation, pointing out that some of the theorems matched what they’d noticed, and some didn’t (particularly the ones involving diagonals.)<\/p>\n

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After, students started the activity I put inside the notes. For each diagram they needed to identify four things:<\/p>\n

    \n
  1. What the shape is (admittedly not too difficult, as there’s only two to choose from.)<\/li>\n
  2. How they know it’s that shape, based on either one of the theorems or the definition of the shape.<\/li>\n
  3. The value of any variables in the diagram.<\/li>\n
  4. How they know it’s that value, again by referencing a theorem or definition.<\/li>\n<\/ol>\n

    \"\"<\/a><\/p>\n

    There is a flaw in these questions. All of the parallelograms have a horizontal pair of sides, while the rhombuses are in a “diamond” position. This made distinguishing the two a little too easy. If I get a chance, I’d like to rotate some of the diagrams to different angles.<\/p>\n

    Downloads for these notes can be found here<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"

    First day back from Christmas break saw my Geometry classes looking at theorems about parallelograms and rhombuses. We’d already looked at definitions of the different types of special quadrilaterals. I had students divide a page in their notebook in two, and told them to rewrite the definitions of the parallelogram and rhombus in those sections. … <\/p>\n

    Continue reading “Parallelogram and Rhombus Theorems”<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[6,3,7,2,4,5],"class_list":["post-346","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-exploragons","tag-geometry","tag-inbs","tag-math","tag-polygons","tag-theorems"],"_links":{"self":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts\/346","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/comments?post=346"}],"version-history":[{"count":7,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts\/346\/revisions"}],"predecessor-version":[{"id":590,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/posts\/346\/revisions\/590"}],"wp:attachment":[{"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/media?parent=346"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/categories?post=346"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.primefactorisation.com\/blog\/wp-json\/wp\/v2\/tags?post=346"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}