Type of Class:
          Standard High School

Related VA SOL: G.5

Time Frame:
         Ninety-minute block period 

Objectives:

  • Students will know how to prove two triangles are similar.

  • Students will know how to prove two triangles are congruent.

  • Students will use practical problems to prove triangles are similar and congruent.

Materials:

  • Graph paper

  • Rulers

  • Protractor

Procedures:

1)      Triangles can be proven similar or congruent by some of the following:

a)      SSS, SAS, ASA, SSA, AAS, AAA, SSA

i)        Explain what each type means with a picture

·        Note: For triangles with angles and sides (SAS, ASA, SSA, AAS, SSA), the three letters must be given in clockwise or counterclockwise order.

      

2)      In groups of three or four, have students construct three pairs of triangles on a piece of graph paper with a ruler and a protractor.

a)      Each pair should represent the SSS, SAS, ASA, SSA, AAS, SSA, AAA properties.

b)      Once finished with all of the constructions, groups will form a conjecture about which properties of congruence can be used to prove two triangles congruent/similar.

c)      Groups will then conjecture about which pairs cannot be used to prove two triangles congruent.

d)      Students will then repeat this process to conjecture which properties can be used to prove two triangles similar.

e)      After all of the groups are finished, the class will come together and form uniform conjectures to use.

 

3)      Word problem:

a)      Ramon places a mirror on the ground forty-five feet from the base of a geyser.  He walks backward until he can see the top of the geyser in the middle of the mirror.  At that point, Ramon’s eyes are six feet above the ground and he is seven and a half feet from the mirror.  Use similar triangles to find the height of the geyser.  

 

  

4)      Explain why the following triangles are similar, and find segment DE.

 

5) Example to be done by groups while the teacher walks around and checks work:

                  

 6) Example to be done by groups while the teacher walks around and checks work:

  

Assessment: Assigned homework to be started in class if time permits.

Suggestions/Comments: This lesson would be more effective if it were to take place immediately following the proofs lesson on introductory congruency and similarity.  Students often have trouble with proofs, which is why it is important for the students to work the examples together in groups.  That way, if one student gets stuck another is there to help out.