This unit will teach included angles and sides, SAS, ASA, AAS, and HL congruency.

First, you must understand what an included angle is.  An included angle is an angle that is between two sides of a triangle.  It likes to have friends and feel included;  the sides are its friends, and the angle is between them. An included side is a side that is between two angles of a triangle.


Now, two triangles can be shown to be congruent if two sides and the included angle between them are the same size.  This is called SAS  congruence. 


A right triangle has a right angle at one vertex.  The side opposite the right angle is called the Hypotenuse.  The remaining two sides are called Legs.


Two right triangles can be shown to be congruent by showing the the lengths of the hypotenuses are the same, and that the length of one of each of the remaining legs are congruent.  This is called HL congruency.


 Try the following worksheet to work on these concepts.  Click on the link below, select chapter 4, and then lesson 4.4:


SAS, HL Worksheet


Now, ASA is another way to show two triangles congruent.  It requires that two angles and their included side be congruent.


AAS uses the requirement that two consecutive angles and one side (connected to the second angle) be congruent.


Try this quiz to practice mastering these concepts.  Click on the link below and do chapter 4, lesson 4.5 and see how you do:


ASA, AAS Worksheet


Now, here is another type of quiz for you to check your mastery of these concepts:


Congruent Triangles; Recognizing


The following activity will give you the chance to create congruent triangles yourself.  Try creating one of each type (SAS, ASA, AAS, HL) in the following link:


Congruent Triangles Construction Using SSS, SAS, ASA


Proofs using these concepts always show if you have mastered the material.  This link will give you tips on completing proofs:


SSS, SAS, ASA Congruent Triangles in Proofs TIPS


You will need to complete 3 proofs on paper to turn into the teacher for credit  Choose from the following proofs with some help from the link below:


SSS, SAS, ASA, HL Congruent Triangles Proofs


One last word of advice.  There is no such thing as SSA congruence.  (This is no joke!)  Spelled backwards, this is not only a dirty word, but it does not show congruence between two triangles!



All done!  Congratulations!  Good luck on the test!