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.
• “¿Qué observan acerca de los triángulos H, L y V?” // “What do you notice about Triangles H, L and V?” (They all have right angles.) 
• “Los triángulos que tienen un ángulo recto son triángulos rectángulos” // “Triangles that have a right angle are right triangles.”
• “¿Cómo supieron si un ángulo de un triángulo es un ángulo recto o no?” // “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.)
• “¿Pueden encontrar otros triángulos rectángulos en el grupo?” // “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: “En nuestro grupo de triángulos, no vimos ninguno que tuviera más de un ángulo recto ni más de un ángulo obtuso. Creen que es posible que un triángulo tenga: // “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:
  • ¿Dos ángulos rectos?” // Two right angles?” (No, two of the sides won’t meet to make a triangle.)
  • ¿Dos ángulos obtusos?” // 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).

• “¿Cómo decidiste si un triángulo era un triángulo rectángulo o no?” // “How did you decide if a triangle was a right triangle or not?”
• “¿Dónde más ves triángulos que pueden tener lados perpendiculares? ¿Qué herramientas podrías usar para saber si son ángulos rectos?” // “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.
• “¿Hubo triángulos que parecían ser triángulos rectángulos, pero que no lo eran, o que parecían no ser triángulos rectángulos, pero que sí lo eran?” // “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.)