The Strength of Triangles

Bridges, Windmills and the Wright Brothers’ Wings

Lesson Plan

Grade level(s): 9-10, (Can be used and adapted for 8th grade level.)

Time frame: 1 day in class (with out-of-class assignment or internet research needed on another day or days)

Subject matter: similar triangles, congruent triangles

Teacher information:

Julie Caluwe Ladwig
Edwardsville High School
Southern Illinois University Edwardsville

jladwig@ecusd7.org

Lesson Plan Description and Rationale:

Students will work in small groups (pairs). Students will begin by creating three dimensional figures using a set of ball and rod magnets, if available (Super Mags, Mega Mags, Geo Mags). Teams will discuss the strength of the figures they make that are based on triangles and those that are not. Each team will then be given the illustrations for the Langley Machine, a flying machine design by the Wright brothers, a bridge and a windmill. Students are to identify all similar and congruent triangles in the figures. They will also write discussions of all the methods for proving triangles similar and congruent as well as a discussion of why each of the constructions is probably based on triangles. Finally, students will identify other constructions that are based on triangles.

State Standards:

STATE GOAL 9: Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.

9.B.4 Recognize and apply relationships within and among geometric figures.

9.A.5 Use geometric figures and their properties to solve problems in the arts, the physical and life sciences and the building trades, with and without the use of technology.

Objectives:

Students will discover that triangles make for a strong base for constructions through experimentation with ball and rod magnets. Students will then analyze photographs of a bridge and a windmill and a plan for a flying machine. Specifically, they will take note of the numerous triangles in the constructions and identify all congruent and similar triangles in each construction using any means necessary and appropriate. Students will discuss, in writing, all ways to prove that triangles are similar or congruent. Finally, students will locate other examples of constructions that use the strength of triangles.

Resources:

	“The Wilbur and Orville Wright Papers--Langley Machine--Drawings and Blueprints,” pg 1. Undated. The Wilbur and Orville Wright Papers. [http://memory.loc.gov/cgi-bin/query/r?ammem/wright: @field(DOCID+@lit(wright002763))] [mwright-04151] (March 2004). Smithsonian Institution--Dispute--Langley Machine--Drawings and Blueprints, undated.
	“Metropolitan West Side Elevated Railway Company elevated bridge with train crossing.” 1911 Feb. 4. Photographs from the Chicago Daily News, 1902-1933. [http://memory.loc.gov/cgi-bin/query/r?ammem/cdn:@field (NUMBER+@band(ichicdn+n05650))] [ichicdn n056530] (March 2004). Chicago Daily News negatives collection, DN-0056530, Courtesy of the Chicago Historical Society.
	Butcher, Solomon D. “Livestock on the James Gates ranch at Gates, Nebraska, showing Gates bridge on the Middle Loup River and T.J. Butcher's home in the distance to the right.” 1888. Prairie Settlement: Nebraska Photographs and Family Letters, 1862-1912. [http://memory.loc.gov/cgi-bin/query/r?ammem/ psbib:@field(DOCID+@lit(p14572))] [nbhips 14572] Nebraska State Historical Society, [Digital ID, e.g., nbhips 14572].

Methods:

Separate students into pairs or small groups (2-3). If possible, begin by giving each group a set of ball and rod magnets with instructions to play around with constructions that are based on triangles and some that do not have any triangles in their structure and to judge the strength of each constructed figure based on how easy it is to crush/flatten/tilt the figure.

If magnets are not available you may want to consider purchasing one boxed set and have students (or yourself) demonstrate constructions in front of the class to accomplish the same goal.

If magnets are not available at all, you could use straws to make constructions that use triangles and polygons by tucking ends into ends and compare the strengths of the shapes by trying to tilt and crush them.

After class discussion on the experiment with the ball and rod magnets (or straws), in which the strength of triangles should be the focus, student teams will each be given a set of the three illustrations for the activity.

Student Directions (click here for printable word document):

IDENTIFICATIONS: Using a ruler and protractor, identify all sets of congruent and similar triangles in each image. Use colored pencils or crayons to identify/code sets of congruent and similar triangles (in other words, color the ones that go together in the same way). You may need to make some notation on the side of each picture to explain your coloring/coding. Be sure to consider the different ways we can prove triangles to be either similar or congruent when you are checking for these relationships. You will turn in all three colored/coded illustrations.

WRITING: On a separate sheet of paper, write two paragraphs in which you describe all the methods that can be used to prove two triangles similar or congruent (one paragraph for each). Mention which methods you used in making decisions in the three pictures.

RESEARCH: You are to locate two other examples of “objects” that are constructed with the strength of triangles in mind (no bridges, windmills, or flying machines). You may find that simple observation of your daily surroundings provides you with examples, or you may want to turn to the internet and/or your family for ideas. Either find a picture or draw a picture of each of your examples. Each picture is to be on a separate sheet of paper and have a caption identifying what the object is and stating that it uses triangles.

Evaluation:

If this activity were to be out of 50 points, I would grade in the following manner:

Magnet/Straw involvement/discussion = 10 points: Did students participate
fully and share discoveries and ideas?

Color Coded Pictures = 15 points (5 per picture): Are all similar and
congruent triangles clearly indicated in each picture?

Writing = 10 points (5 per paragraph): Were all methods discussed for
proving similarity and congruence? Was good grammar used?

Research = 10 points (5 per example): Did student find examples of
triangle use?

Teamwork = 5 points: Did student do his/her share of the work and
work well with his/her team?

Key words for this lesson: similar triangles, congruent triangles