Lesson 10

Discover

 

To construct the windows for the roof of the National Gallery of Canada, the manufacturer needed accurate measurements. For the rectangular windows, only two measurements were needed. The manufacturer needed to know the length and width of the rectangular windows in order to create congruent rectangles. To construct the triangular windows, six measurements could have been provided—three side lengths and three angles. But are all six measurements required to construct congruent triangles?

 

Actually, the manufacturer only needed to know three measurements to create the congruent triangles for the gallery’s roof. There are several different combinations of three measurements that could have been given to the manufacturer.

• side-side-side (SSS)
• side-side-angle (SSA)
• side-angle-side (SAS)
• angle-side-angle (ASA)
• angle-angle-side (AAS)
• angle-angle-angle (AAA)

Not all of these combinations of measurements will guarantee that a congruent triangle is produced. So which three measurements must be given to the manufacturer in order to produce congruent triangles?

 

Try This 1

 

Use the applet Creating Congruent Triangles to see triangles created given AAS and AAA.

 

 

The applet Congruent Triangles Manipulative1 can be used to create triangles given SSS, SAS, ASA, and SSA.

Use the information you collect from these two applets to answer the following questions.

1. Which combination(s) of given side and angle measurements ensure that all the triangles produced are congruent?
   
   
2. Which combination(s) of given side and angle measurements do not ensure that the triangles are congruent? (Is it possible to construct two non-congruent triangles with some combinations of sides and angles?)

Self-Check 1

 

Based on your findings from Try This 1, complete the Congruent Triangle Table.

 

 

1 National Library of Virtual Manipulatives. © 2011 Utah State University