The purpose of this activity is for students to describe and sort triangles based on the length of their sides and the size of their angles. Students are asked to find all the triangles (from the same set of cards used in the previous lesson) that have specific attributes. When students choose rulers, square corners, or protractors to identify and compare attributes of triangles, they use appropriate tools strategically (MP5).

Along the way, students notice attributes that all triangles seem to share (for instance, having three angles and at least two acute angles), attributes that some triangles share (for instance, having two equal angles or two equal sides), and those that no triangles seem to have (for example, parallel sides or multiple obtuse angles). With these repeated observations, students deepen their understanding of the properties of triangles and their sub-groups (MP8).

In the Activity Synthesis, students are introduced to right triangles.

• Add new vocabulary and sketches to the chart from the previous lesson.
• “What do you notice about Triangles H, L and V?” (They all have right angles.) 
• “Triangles that have a right angle are right triangles.”
• “How did you know whether an angle in a triangle is a right angle?” (I measured it with a protractor or an object with a square corner.)
• “Can you find other right triangles in the set?” (Triangle Y)
• Invite students to share their completed sentences for the last question. Record their responses and invite the class to agree or disagree.
  • Some triangles . . .
  • All triangles . . .
  • No triangles . . .
• If time permits, consider asking: “In our set of triangles, we didn’t see any with more than one right angle or more than one obtuse angle. Do you think it’s possible for a triangle to have:
  • Two right angles?” (No, two of the sides won’t meet to make a triangle.)
  • Two obtuse angles?” (No, two of the sides won’t meet to make a triangle.)

In this activity, students identify right triangles. They also explain why certain given shapes are not right triangles. As they determine whether a triangle is a right triangle, students may use the corner of an index card or a piece of paper, use a protractor, or trace an angle in a triangle to compare it with an angle that they know to be a right angle. In doing so, students practice choosing tools strategically (MP5).

• “How did you decide if a triangle was a right triangle or not?”
• “Where else do you see triangles that may have perpendicular sides? What tools could you use to determine if they are right angles?”

• Invite students to share their responses and how they found the right triangles in the set.
• “Were there any triangles that appeared to be right triangles but are not, or don’t appear to be right triangles but are?” (Triangle H looks like one but isn’t.)