Lesson 10

Lesson 10: Congruent Triangles

 

Focus

 

The National Gallery of Canada building in Ottawa contains both similar and congruent triangles in its roof design. The smaller congruent triangular windows at the top of the building fill a larger similar triangular steel frame. For the smaller triangles to be congruent, the lengths of the corresponding sides and the measures of the corresponding angles of each of the smaller triangles must be the same. For the two sizes of triangles to be similar, the length of the sides of the larger triangular steel frame have to be proportional to the smaller triangles and the angle measures have to be the same.

 

When items are part of a larger design, such as the windows in the National Gallery of Canada, it is crucial that all the necessary measurements are provided to the manufacturers. If the manufacturer is not given enough information, the design will not be accurately reproduced.

 

For instance, the company that made the windows for the National Gallery of Canada had to have enough information to ensure that every window constructed was congruent. If the notes were not the same, the smaller triangles would not have fit into the larger steel frame. The entire construction process would have been affected, and the overall design would not have worked.

 

This lesson will help you answer the following inquiry questions:

• What is the minimum amount of information needed to create two triangles that are congruent?
• How can deductive reasoning be used to prove that triangles are congruent?

Assessment

• Try This 2

All assessment items you encounter need to be placed in your course folder.

 

Save a copy of the Lesson 10 Assignment to your course folder.

 

Materials and Equipment

• ruler or straightedge
• compass
• protractor (You may find it helpful to use Virtual Tools.)