The purpose of this activity is to sort triangles according to their angle measures and side lengths. When they finish sorting, students will notice that two of the possible categories will not have any matching triangles, namely if all 3 sides of a triangle have the same length then the triangle will not have a right angle or an obtuse angle. Students think about whether or not such a triangle could exist and present informal arguments to explain their reasoning (MP3). The Activity Synthesis formally introduces the category of right triangles.

• Display a set of triangle cards and a blank table from the student book. Place the cards in the correct location in the table as you discuss the questions.
• “How did you determine which triangles have 90 degree angles?” (I used the corner of a sheet of paper, measured it using a protractor, or used the grids.)
• “Triangles with a 90 degree angle are called right triangles.”
• “How can we be certain that a triangle is a right triangle?” (We can measure the angles or use the grid.)
• Display Shape F.
• “What do you notice about the angles of this triangle?” (One is a 90 degree angle and the other two are equal to each other. The other two are half of a 90 degree angle.)
• “What do you notice about the sides of this triangle?” (Two of them are the same length.)

The purpose of this activity is for students to sort triangles in a way that makes sense to them and then make observations about right triangles. Students make statements about the right triangle shape cards using the quantifiers all, some, or none. The main shape characteristics students will likely use in their statements are the angle measures, particularly for the two angles that are not right angles, and the side lengths. Students might also choose other characteristics like the orientation of the triangles.

This activity uses MLR7 Compare and Connect. Advances: Representing, Conversing.

• Invite students to share how they sorted the cards, including
  • Triangles with a right angle
  • Triangles with an obtuse angle
  • Triangles with acute angles
  • Triangles with no sides equal
  • Triangles with 2 or more sides equal
• “How did you know which triangle cards have right triangles?” (I used the grid lines. I measured the angles with a protractor. I used the corner of a card.)
• Invite students to share their responses for properties all of the right triangles share.
• Record their responses.