Adding the Angles in a Triangle
10 min
Teacher Prep
Setup
Narrative
The purpose of this activity is for students to recall properties and types of triangles and specific language for describing them. In this activity, students draw a variety of triangles and sort them into categories of their choosing. Monitor for students choosing categories that compare angle measures and side lengths. Students may use informal language to describe their categories, such as “all of the sides are different lengths” rather than “scalene.”
Select students who use these categories to share during the whole-class discussion:
- Equilateral triangles
- Right triangles
- Isosceles triangles
- Obtuse triangles
Launch
Arrange students in groups of 4. Distribute 3 sticky notes per student. Give 1 minute of quiet work time for students to draw a triangle on each sticky note.
Tell each group to look at all of their triangles and sort them into categories. Give 2–3 minutes of group time followed by a whole-class discussion. Listen for language describing the side lengths and angles of triangles, such as “equilateral,” “right,” “obtuse,” and “acute.”
Student Task
Sample Response
Answers vary
Activity Synthesis (Teacher Notes)
Invite previously selected students to share the categories they chose for the triangles. As students describe categories, organize their descriptions for all to see in a table or chart like this one:
| acute (all angles acute) | right (has a right angle) | obtuse (has an obtuse angle) | |
|---|---|---|---|
|
scalene (side lengths all different) |
|||
|
isosceles (at least two side lengths are equal) |
|||
|
equilateral (three side lengths equal) |
As students share, invite them to place their sticky note on the chart for all to see.
If any students drew triangles that fall under multiple categories, such as a right isosceles triangle, display it for all to see. If not, draw one for all to see. Ask students which categories the triangle belongs to. Students may describe an isosceles triangle as having two angles the same or two sides the same.
Ask students if they can draw any other triangles that fit into two categories. Examples include equilateral and acute, scalene and obtuse, scalene and right. Students may describe scalene as having all different side lengths or all different angles.
Ask students if it is possible to draw an equilateral triangle that has a right angle. (No, 3 right angles would not form a triangle, and all the angles are the same in an equilateral triangle.)
If time allows, continue filling out the table with an example of each type of triangle or an explanation of why that triangle is not possible.
Standards
- 7.G.2·Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
- 7.G.A.2·Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
25 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Adding the Angles in a Triangle
10 min
Teacher Prep
Setup
Narrative
The purpose of this activity is for students to recall properties and types of triangles and specific language for describing them. In this activity, students draw a variety of triangles and sort them into categories of their choosing. Monitor for students choosing categories that compare angle measures and side lengths. Students may use informal language to describe their categories, such as “all of the sides are different lengths” rather than “scalene.”
Select students who use these categories to share during the whole-class discussion:
- Equilateral triangles
- Right triangles
- Isosceles triangles
- Obtuse triangles
Launch
Arrange students in groups of 4. Distribute 3 sticky notes per student. Give 1 minute of quiet work time for students to draw a triangle on each sticky note.
Tell each group to look at all of their triangles and sort them into categories. Give 2–3 minutes of group time followed by a whole-class discussion. Listen for language describing the side lengths and angles of triangles, such as “equilateral,” “right,” “obtuse,” and “acute.”
Student Task
Sample Response
Answers vary
Activity Synthesis (Teacher Notes)
Invite previously selected students to share the categories they chose for the triangles. As students describe categories, organize their descriptions for all to see in a table or chart like this one:
| acute (all angles acute) | right (has a right angle) | obtuse (has an obtuse angle) | |
|---|---|---|---|
|
scalene (side lengths all different) |
|||
|
isosceles (at least two side lengths are equal) |
|||
|
equilateral (three side lengths equal) |
As students share, invite them to place their sticky note on the chart for all to see.
If any students drew triangles that fall under multiple categories, such as a right isosceles triangle, display it for all to see. If not, draw one for all to see. Ask students which categories the triangle belongs to. Students may describe an isosceles triangle as having two angles the same or two sides the same.
Ask students if they can draw any other triangles that fit into two categories. Examples include equilateral and acute, scalene and obtuse, scalene and right. Students may describe scalene as having all different side lengths or all different angles.
Ask students if it is possible to draw an equilateral triangle that has a right angle. (No, 3 right angles would not form a triangle, and all the angles are the same in an equilateral triangle.)
If time allows, continue filling out the table with an example of each type of triangle or an explanation of why that triangle is not possible.
Standards
- 7.G.2·Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
- 7.G.A.2·Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.