As the students walk in, I hand them a slip of paper with three diagrams. Students look at pairs of triangles and write congruency statements for each pair of triangles based on information shown in the diagrams.
The pairs of triangles shown in the Do Now will be used later in the lesson to show how triangles are congruent by Side-Side-Side, Side-Angle-Side, and Angle-Side-Angle. When students finish writing their statements, they cut out the diagrams to use them for the graphic organizers they will be creating later in the lesson.
For the Mini-Lesson, students will create a Three-Tab Organizer. On the front of the organizer, students will write SSS on the first tab, SAS on the second tab, and ASA on the third tab. We discuss what the abbreviations stand for and then students identify which postulate can be used to prove the triangles from the Do Now are congruent. Students then glue the diagrams onto the back of the correct tab (see the file “SSS, SAS, and ASA Activity”).
Students continue working on their graphic organizers by writing definitions of the postulates. For example, “If all sides in one triangle are congruent to all sides in another triangle, the triangles are congruent.” They then use their congruence statements from the Do Now to describe how the triangles are congruent. The definition and description can be written on the bottom sections of the organizer.
Students work individually to decide if there is enough information to prove four pairs of triangles on a worksheet are congruent to each other. If there is enough information, students state the postulate that proves the triangles are congruent. If there isn’t enough information, students identify what would need to be congruent and state the postulate that proves the triangles are congruent. Students can use their graphic organizers to help them answer the questions.
After about 7 minutes, we go over their answers. There can be different answers for questions 2 and 3. The triangles in question 2 can be made congruent by SAS or ASA depending on the information given. For question 3, some students may recognize that segment AE is in both triangles and is congruent to itself, and therefore the triangles are congruent by SAS. Other students may identify that more information is needed and show that angle D is congruent to angle F, which proves the triangles are congruent by ASA.
As a summary, we discuss why triangles cannot be proven congruent by SSA. I first show a video demonstrating the concept. Then students are asked to write an explanation in their notebook about why two triangles cannot be congruent if two of their corresponding sides and an angle not included between those sides are congruent to each other.
When students think about why Side Side Angle doesn’t work, they often figure out the SSA can be called Angle Side Side. Sometimes this realization helps students to remember that triangles cannot be proved congruent using SSA.